Answers by visitors named: MathGuru

Here's one way to do this problem: n = 10 p = 400/10000 = .04 q = 1 - p = 1 - .04 = .96 You will need to find P(2) through P(10). Add those values for your probability. You can use a binomial probability table, or calculate by hand using the following for...

18 years ago

You can also take 1 - [P(0) + P(1)], which is easier than finding P(2) through P(10). This way you will just need to find P(0) and P(1). Either way you can still use a binomial probability table or calculate by hand. I hope this will also help.

18 years ago

Yes, you will need to find n. Since P(x) = 0.1 and x = n, you can solve for n using logarithms and the binomial probability function: P(x) = (nCx)(p^x)[q^(n-x)] Using what is known: 0.1 = (1)(0.75^x)(0.25^0) Using logarithms, solve for n: log(0.1) = n log...

18 years ago

SST = ∑X^2 - (∑X)^2/N ...where ∑X^2 = sum of squared scores and (∑X)^2 = square of the summed scores. N = total sample size. SSM = ∑A^2/n - (∑X)^2/N ...where A^2 = square of the sum of scores in each group and n = sample size per group. SSE = ∑X^2 - ∑A^2/...

18 years ago

Confidence interval using proportions: CI98 = p + or - (2.33)(sqrt of pq/n) ...where + or - 2.33 represents 98% confidence using a z-table. (q = 1 - p ...and... n = sample size) I hope this helps.

18 years ago

Your data: X P(X) 0 0.50 1 0.41 2 0.05 3 0.04 Here's a formula for the mean: SUM[X * P(X)] (Take each X times its respective P(X), then sum for a total. This will be your mean.) Here's a formula for the standard deviation: SQRT of {SUM[X^2 * P(X)] - mean^...

18 years ago

Find P(0), then take 1 - P(0) for your probability (since the problem says "what is the probability that at least one" is defective). Using the binomial probability function (you can use a binomial probability table as well): P(x) = (nCx)(p^x)[q^(n-x)] n...

18 years ago

If I'm interpreting this question correctly, you may be looking for independent and dependent variables as one possible answer.

17 years ago

It helps to know how to read a z-table to answer these kinds of questions. For part A, you will need to find a z value where 80% is below the z and 20% is above the z. Remember that the mean divides the distribution in half: 50% is below the mean and 50%...

18 years ago

Did you copy this problem correctly? Do you mean this: (6p-18)/9p divided by (3p-9)/(p^2 + 2p) If so: (6p-18)/9p * (p^2 + 2p)/(3p-9) 6(p-3)/9p * p(p + 2)/3(p-3) -->you have this step. Cancel out common factors. When you do that, you are left with: 2(p + 2...

18 years ago

You can use a one-sample z-test on this data. Null hypothesis: Ho: µ = 3 -->meaning: population mean is equal to 3 minutes Alternate hypothesis: Ha: µ < 3 -->meaning: population mean is less than 3 minutes Using the z-test formula to find the test statist...

17 years ago

The student is correct. Can you determine why? (Hint: Categorical data is also called nominal data or qualitative data.)

18 years ago

Here's one way to do this problem; there may be others. Using the normal approximation to the binomial distribution, we have the following: p = .5 q = .5 --> q = 1 - p x = 60 n = 100 We now need to find mean and standard deviation. mean = np = (100)(.5) =...

18 years ago

Since your sample size is small and the problem doesn't say that the population has a normal distribution, you may want to use a t-table to determine the 95% confidence interval. A general example of a formula is: CI95 = mean + or - (t-value)(sd/√n) Note:...

18 years ago

One other comment: if you are expected to use a z-value instead of a t-value, the z-value would be 1.96 using a z-table for a normal distribution.

18 years ago

Algebraic equation: z = kyx^3 Substituting: 96 = k(6)(2)^3 96 = 48k 2 = k Therefore: z = 2yx^3

18 years ago

I'll explain 2 of these questions; see if you can figure out the other two. 4.1 The mean will be changed and the standard deviation will remain the same. There will be no change in standard deviation since each score and also the mean increase by constant...

17 years ago

The "short" method: ∑(x - µ)^2/N ...where ∑ means to sum or add up, µ = population mean, and x = each piece of individual data. The numerator in the "short" method ∑(x - µ)^2 is called the Sum of Squares, which can also be written as: ∑x^2 - (∑x)^2/N Now...

17 years ago

Let's set up the null and alternative hypothesis, find a formula to use, then go from there. Null hypothesis: Ho: p = .42 -->meaning: population proportion is equal to .42 Alternative hypothesis: Ha: p > .42 -->meaning: population proportion is greater th...

17 years ago

Let's set up a null and alternative hypothesis, find a formula, then go from there. Null hypothesis: Ho: µ = 20.5 -->meaning: population mean is equal to 20.5 Ha: µ < 20.5 -->meaning: population mean is less than 20.5 Using the z-test formula to find the...

17 years ago

Example of a proportional confidence interval formula: CI99 = p + or - (2.58)[√(pq/n)] ...where p = x/n, q = 1 - p, and n = sample size. Note: + or - 2.58 represents 99% confidence interval. You will need to find the z-value for the 90% interval in the pr...

17 years ago

Correction: q = .68

17 years ago

Hypotheses: Ho: pY = pR (R = red trucks; Y = yellow trucks) Ha: pY < pR You can use a binomial proportion 2-sample z-test for this kind of problem. Here is one formula for this type of test: z = (pY - pR)/√(pq(1/n1 + 1/n2) p = (x1 + x2)/(n1 + n2) q = 1 -...

17 years ago

I used an online calculator and came up with this: y = a + bx where: a= -15.4 b= 14.4 r = 0.978 Your formula looks correct. It's easy to make errors with the calculations when doing these kinds of problems.

17 years ago

The variables m or n cannot be equal to 0. (You cannot have a 0 in the denominator.) 4/mn * m/2 = 4m/2mn Reduce the fraction. (Hint: common factors in the numerator and denominator are 2 and m.) I hope this will help.

17 years ago

What you have here is the sum of two angles, which is: sin(c+h) = sin(c)cos(h) + cos(c)sin(h) I'm not sure where the "x" comes into play with your equation, is it supposed to be a variable or a multiplier?

17 years ago

You'll need to calculate the mean and standard deviation from your data. These values will be needed in the following formula: t = (sample mean - population mean)/(standard deviation divided by the square root of the sample size) Note: T-tests can be used...

17 years ago

Using the normal approximation to the binomial distribution, let's look at the information given to you in the problem. Your values are the following: p = .01, q = 1 - p = .99, x = 10, and n = 1500 We need to find mean and standard deviation. mean = np =...

17 years ago

You might try this formula for your chi-square test: Chi-square = (n - 1)(sample variance)/(value specified in the null hypothesis) n = 15 sample variance = 72.7 value specified in the null hypothesis = 60 Chi-square = (15 - 1)(72.7)/60 Finish the calcula...

17 years ago

Here's the formula I would use for this type of problem: CI82 = mean + or - 1.35(sd / √n) ...where + or - 1.35 represents the 82% confidence interval, sd = standard deviation, √ = square root, and n = sample size. With your data: CI82 = 258.5 + or - 1.35...

17 years ago

This appears to be a hypothesis test involving inferences concerning two variances (standard deviation is the square root of the variance). Sample 1: n = 25; variance = sd^2; df = n - 1 = 24 Sample 2: n = 25; variance = sd^2; df = n - 1 = 24 Note: sd = st...

17 years ago

Happy to help. Good job! :)

17 years ago

A t-distribution is sensitive to the size of the sample when considering confidence intervals. If a z-distribution is used instead of a t-distribution with small sample sizes, the confidence interval may be too narrow and the ability to estimate the true...

17 years ago

You can also use a binomial proportion 2-sample z-test for this type of problem. Look at my response to your previous post to see how to set up this problem. Remember that this will also be a one-tailed test.

17 years ago

Divide by the square root of the sample size in this case since the problem is looking to find the probability for the sample mean. 20 - 20.21 / .12/√24 -->note the sample size is 24. I hope this will help.

17 years ago

OK, since x = acres of land and A = acres of land, solve the least squares regression formula for x. Your formula will then be x =... instead of y = ... Once you have solved the regression formula for x, you will then be able to substitute 1.2P for x beca...

17 years ago

Try this formula: n = [(z-value)^2 * p * q]/E^2 = [(2.33)^2 * .397 * .603]/.035^2 I'll let you finish the calculation. Note: n = sample size needed; .397 (which is approximately 278/700 in decimal form) for p and .603 (which is 1 - p) for q. E = maximum e...

17 years ago

Do you know what the variable x represents in the least squares regression formula? If x represents the same variable as one of the variables in the formula A = 1.2P, then you might be able to set the formulas equal to each other by solving for the same v...

17 years ago

Let's try the binomial probability function, which states: P(x) = (nCx)(p^x)[q^(n-x)] For a): n = 15; x = 15 * .2 = 3; p = .2; q = 1 - p = 1 - .2 = .8 Therefore: P(3) = (15C3)(.2^3)(.8^12) = ? Can you take it from here to finish? For b): n = 15; x = 0; p...

17 years ago

Synthetic division is one way to find your factors. Here's how this one works out: 2| 1 -6 12 8 ..... 2 -8 8 .. 1 -4 4 0 Therefore: (x - 2)(x^2 - 4x + 4) Factors of (x^2 - 4x + 4) are (x - 2)(x - 2) Factors are: (x - 2)(x - 2)(x - 2) or (x - 2)^3 I hope t...

17 years ago

Both parts are using one-sample two-tailed tests. Since the sample in part a) is so small, you can try a one-sample t-test and for part b), a one-sample z-test. For the t-test: t-statistic = (sample mean - population mean)/(standard deviation divided by t...

17 years ago

You can use a proportional confidence interval formula for large samples. Here's one: CI99 = p + or - (2.58)[√(pq/n)] ...where p = x/n; q = 1 - p; + or - 2.58 represents the 99% confidence interval using a z-table. Substituting into the formula, we have t...

17 years ago

Try this formula: n = [(z-value)^2 * p * q]/E^2 = [(2.33)^2 * .8 * .2]/.03^2 I'll let you finish the calculation. Round to the next highest whole number. Note: n = sample size needed; .8 for p and .2 for q (q = 1 - p). E = maximum error, which is .03 (3%)...

17 years ago

OK, let's look at what you have and what you need in table form: ............ SS ...... df ..... MS ..... F Between..... ? ....... 2 ...... 20 ..... 4 Within...... ? ....... 42 ..... ? Total ...... ? ....... 44 To find SS between, take df between times MS...

17 years ago

Formula for 99% interval estimate of the population mean: CI99 = mean + or - 2.575(sd/√n) ...where + or - 2.575 represents the 99% confidence interval using a z-table, sd = standard deviation, √ = square root, and n = sample size. Substitute what you know...

17 years ago

Let me give you a little background and maybe this will help you understand a few of the concepts of hypothesis testing. We use samples to support some hypothesis about a population. We make inferences about the population from sample data. When setting u...

17 years ago

Use z-scores. z = (x - mean)/sd With your data: z = (78 - 68.2)/10.4 = 0.94 .1736 is the probability using a z-table for a single student with a score greater than 78. Now we can use a normal approximation to the binomial distribution. mean = np = (75)(.1...

17 years ago

What do the variables in the formula A = 1.2P represent? Once you know what the variables represent, it may help with your next step.

17 years ago

Let's try a binomial proportion one-sample z-test for this problem. I'll give you the setup for the calculations and let you take it from there. Formula with your data included: z = (.82 - .9)/√[(.9)(.1)/100] Note: .82 is 82/100; .9 is 90% from the proble...

17 years ago

Already answered in another post. :D

17 years ago

Here are a few hints. Step 1: Look at the values of each set of test scores (test score of student with cat versus test score of student without cat). Assign a minus if the scores decreased; assign a plus if the scores increased. Assign a 0 for those who...

17 years ago

You will need to use the z-score formula and a z-table to answer these questions. The formula: z = (x - mean)/sd -->sd = standard deviation For a) and b), find z using the formula. Then determine the percentage using the z-table. For c) and d), find x usi...

17 years ago

Null hypothesis: Ho: p = .95 -->meaning: population proportion is equal to .95 Alternative hypothesis: Ha: p > .95 -->meaning: population proportion is greater than .95 Using a formula for a binomial proportion one-sample z-test with your data included, w...

17 years ago

Here might be one way to do this problem: Null hypothesis is that the coin is fair. Ho: p = .5 Alternate hypothesis is that the coin is unfair. Ha: p not equal to .5 Using the binomial formula: P(x) = (nCx)(p^x)[q^(n - x)] ...where n = number of coin toss...

17 years ago

Ho: µ ≤ 10 -->null hypothesis Ha: µ > 10 -->alternative hypothesis Using the z-test formula to find the test statistic: z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size) z = (14.44 - 10)/(4.45/sqrt of 3...

17 years ago

The probability of making a Type II error is equal to beta. A Type II error is failure to reject the null when it is false. The power of the test is 1-beta and is the correct decision of rejecting the null when it is false. The alpha level directly affect...

17 years ago

Correction (this does not change the outcome): Using the binomial formula: P(x) = (nCx)(p^x)[q^(n - x)] ...where n = number of coin tosses, x = number of times came up heads, p = probability given in the null hypothesis, q = 1 - p. Using your data: P(38)...

17 years ago

Here is one formula you might use for this problem: n = [(z-value)^2 * p * q]/E^2 With your data: n = [(2.575)^2 * .45 * .55]/.10^2 I'll let you finish the calculation (round to the next highest whole number). Note: n = sample size needed; .45 for best es...

17 years ago

For correlation, r^2 is a measure of effect size. It's the correlation coefficient squared and basically represents the proportion of variability that is shared by two variables. The r^2 value may show this effect to be strong or weak. As an example, supp...

17 years ago

Here's a few hints to get you started: a. Find the z-scores. Use the formula: z = (x - mean)/sd z = (400 - 500)/100 = ? z = (675 - 500)/100 = ? Once you have the two z-scores, look at the z-table to determine the probability between those two scores. b. C...

17 years ago

With a 95% confidence interval, one can be 95% confident that the true value of p is contained within that interval. If you calculate the mean and standard deviation of the z-scores, the mean of the z-distribution will be zero and the standard deviation w...

17 years ago

Formula: CI99 = mean + or - 2.575(sd/√n) ...where + or - 2.575 represents the 99% confidence interval using a z-table, sd = standard deviation, and n = sample size. I hope this will get you started.

17 years ago

Since you are already given the values for the confidence interval, take those values, add them together and divide by 2. This will be the proportion of the sample used to generate the interval. A 90% interval means that you can be 90% sure that the popul...

17 years ago

Hypotheses: Ho: µ2001 = µ2000 Ha: µ2001 < µ2000 You will need to use a 2-sample formula for this type of test. You have all the data needed for both samples. This is a one-tailed test because the alternative hypothesis is showing a specific direction. If...

17 years ago

You may want to check this, but I would lean towards d) because a) and c) are saying the same thing. If the null is rejected, then the alternative would be accepted. Usually when doing an F-test and the null is rejected, it is often necessary to do additi...

17 years ago

You may want to check this with a statistics text, but here is one way you might approach this problem. This looks like a hypothesis test involving two variances (standard deviation is the square root of the variance). The null hypothesis would be the rat...

17 years ago

Try a one-sample z-test for your problem. Using the z-test formula to find the test statistic: z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size) z = (3.69 - 3.65)/(.24/√45) Finish the calculation. Use a...

17 years ago

Use z-score formula to find the missing values. z = (x - mean)/sd sd = standard deviation First you have to figure out the mean and standard deviation. Let's look at the values you were given. Between 64 and 79 is one standard deviation (1.8 - .8 = 1.0)....

17 years ago

This looks within range. There may be differences due to rounding when using a confidence interval formula.

17 years ago

To find expected values for each cell, here is a formula you can use: E = (row total)(column total)/n ...where E is the expected cell count if the null hypothesis is true. The null hypothesis states the variables are unrelated in the population. The alter...

17 years ago

If you are doing a z-test, you look at a z-table for your cutoff or critical value(s). How do you translate .08 to a cutoff value from the table? It depends on whether the test is one-tailed or two-tailed. For a two-tailed test (cutoff points at both tail...

17 years ago

Let's gather the data: Height (x): mean = 69, sd = 3 Weight (y): mean = 190, sd = 42 Correlation: r = 0.41 Regression equation is in this format: predicted y = a + bx ...where a = intercept and b = slope. To find the equation, you need to substitute the i...

17 years ago

Calculations for a hypothesis test depend on what kind of test you are doing. There are many different kinds of tests. The significance level is used to reject or fail to reject the null hypothesis in a hypothesis test. If you use a z-table for a one-tail...

17 years ago

A few hints to get you started: 1. If H1 shows a specific direction, the test is one-tailed. If H1 does not show a specific direction (could be in either tail of the distribution curve), the test is two-tailed. 2. Use a one-sample z-test formula to determ...

17 years ago

Try using the binomial probability formula or the binomial probability table. Using a binomial probability table is much easier. For a): n = 20; x = 0, 1, 2, 3, 4, 5, 6; p = .20 When you find the probabilities for each x, add all of them together for your...

16 years ago

If you are doing something like interviews using qualitative methods, you may want to go with smaller sample sizes to develop a more in-depth study. If you are doing something like experiments using quantitative methods with samples from a particular popu...

16 years ago

See my response to your other post on this question.

16 years ago

Use z-scores and a z-table for this problem. Because you are given a sample size, you will need to include the sample size in the calculation: z = (x - mean)/(sd/√n) For a): This will be very close to 100% chance that the average of the draws will be in t...

16 years ago

Ho: µ ≥ 3000 -->this is the null hypothesis. Ha: µ < 3000 -->this is the alternate or alternative hypothesis. You can use a one-sample t-test formula for this problem since the sample size is less than 30. Using a t-table at 0.05 level of significance for...

16 years ago

Critical value decreases if N is increased.

16 years ago

You wrote: How do I write at most 20 and at least 25? At most 20: P(x ≤ 20) At least 25: P(x ≥ 25) Someone else may be able to help you with the function.

16 years ago

Use z-scores and the z-distribution table for this problem. Formula: z = (x - mean)/sd -->sd is standard deviation. With your data: z = (79 - 75)/8 I'll let you finish the calculation. Once you have the z-score, check the z-table for your probability. Rem...

16 years ago

Here's one formula you can use for a problem of this type: n = [(z-value)^2 * p * q]/E^2 Note: n = sample size needed; ^2 = squared; .4 for p and .6 for q (q = 1 - p). E = maximum error, which is .035 (3.5%) in the problem. Z-value is found using a z-tabl...

16 years ago

I'll give you a hint. The mean is a measure of central tendency. Standard deviation is a measure of ___. I hope this will help.

16 years ago

Coefficient of Determination is explained variation divided by total variation (or more simply, the correlation coefficient squared). To find the correlation coefficient, take the square root of .74 for your answer. The Coefficient of Determination shows...

16 years ago

Here's a hint: 4,000 registered voters is the sample size. Can you now determine the population of interest?

16 years ago

One other comment: Explained variation in this case is the variation in Y values that is explained by X values; unexplained variation is variation in Y values that cannot be explained by X values. Total variation is explained values plus unexplained value...

16 years ago

Here's what you will need to answer this question: Lower limits = mean - 3(sd/√n) Upper limits = mean + 3(sd/√n) sd = standard deviation n = sample size You will need to calculate the mean and standard deviation from the data given. Once you have those va...

16 years ago

Pre-exam: mean = 275, sd = 26 Final exam: mean = 71, sd = 6 Correlation: r = 0.67 Regression equation is in this format: predicted y = a + bx ...where a = intercept and b = slope. To find the equation, you need to substitute the information given in the p...

16 years ago

Here's one way that might help you determine positive and negative correlations. With positive correlations, when one thing goes up, the other thing goes up. With negative correlations, when one thing goes up, the other goes down. With no correlation, the...

16 years ago

Yes.

16 years ago

I'll give you a few hints: One is true; two are false. The two false statements are false because of one word in each statement.

16 years ago

This will be within two standard deviations of the mean. To show this, use z-scores. Formula is this: z = (x - mean)/sd Therefore: z = (75 - 95)/10 = ? z = (115 - 95)/10 = ? I'll let you finish the calculations. Remember that one z-score is below the mean...

16 years ago

The probability of making a Type II error is equal to beta. A Type II error is failure to reject the null (Ho) when it is false. The power of the test is 1-beta and is the correct decision of rejecting the null when it is false. The alpha level directly a...

16 years ago

I'll give you several tips to get started on this one and let you take it from there. Null hypothesis: Ho: p = .44 -->meaning: population proportion is equal to .44 Alternative hypothesis: Ha: p > .44 -->meaning: population proportion is greater than .44...

16 years ago

Formula: n = [(z-value) * p * q]/E^2 ...where n is the sample size you seek, z-value is obtained using a z-table for the confidence interval (90%) in the problem, p and q represent proportions, E is the maximum error, and ^2 means squared. Substituting va...

16 years ago

I'll give you a few hints for 1). Rethink part a). The statement says "no more than $300" which means $300 or less. You are correct in that this one is a one-tailed test. Part b) looks good! For part c): The statement is says "at least 1200" which means 1...

16 years ago

If I'm interpreting this problem correctly and since the suggestion is to approximate the distribution by using the Gaussian (or normal) distribution, I would first find the z-score equated to 1% using a z-table. That would be -2.33 (below the mean of the...

16 years ago

I'm not sure if this is what the question is asking, but you might want to check out "power transformation" as a possibility.

16 years ago

Use this formula to find z: z = (x - mean)/(sd/√n) With your data: z = (85.8 - 83)/(16/√64) = ? Once you have the z-score, look at the z-table to determine your probability. I hope this will help get you started.

16 years ago

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