Question

You have been hired as the quality control office of a pharmaceutical company that manufactures aspirin tablets. According to the quality assurance protocol, your job is to do the following. For each shipment of possibly thousands and thousands of aspirin tablets, randomly select and test 300 tablets, then accept the batch if there is no more than 13 tablets that don’t meet the test specification. If, at the pharmaceutical company, the probability that randomly selected tablet is defective is .04, what is the probability that a randomly selected shipment of 300 tablets will be accepted?

What is the probability that a randomly selected sample contains 20 that do not meet the requirements?
Is the value 20 unusual (from a above)

Answer 1

1.Given that you were taking the following measurements, determine if they are discrete or continuous.
a. 10, 20, 20, 25, 30, 34, 37, 40
b. 0.5, 1, 2, 3, 4, 4.2, 4.4, 4.5, 8
2. Suppose that in a population of voters in a certain region 38% are in favor of particular bond issue. Nine hundred randomly selected voters are asked if they favor the bond issue. Find the probability that the sample proportion computed from a sample of size 900 will be within 5 percentage points of the true population proportion.
3. An online retailer claims that 90% of all orders are shipped within 12 hours of being received. A consumer group placed 121 orders of different sizes and at different times of day; 102 orders were shipped within 12 hours.
a. Compute the sample proportion of items shipped within 12 hours.
b. Assuming the retailer’s claim is true, find the probability that a sample of size 121 would produce a sample proportion so low as was observed in this sample.
c. Based on the answer to part (ii), draw a conclusion about the retailer’s claim.
4.Suppose you do a study of acupuncture to determine how effective it is in relieving pain. You measure sensory rates for 15 subjects with the results given. Use the sample data to construct a 95% confidence interval for the mean sensory rate for the population (assumed normal) from which you took the data. The collected data was as follows; 8.6, 9.4, 7.9, 6.8, 8.3, 7.3, 9.2, 9.6, 8.7, 11.4, 10.3, 5.4, 8.1, 5.5, 6.9
a. Find the z score for α = .04 for;
b. A left-tailed test on a standard normal distribution curve.
c. A right-tailed test on a standard normal distribution curve.
d. A two-tailed test on a standard normal distribution curve.
e. Find the t score for α = .05 for a sample size of 25 and degrees of freedom of 24. Assume an approximately normal distribution.
i. A left-tailed t test
ii. A right-tailed t test.
iii. A two-tailed t test.
5.The football coach randomly selected 10 players and timed how long each player took to perform a certain drill. The drill times in minutes were: 9, 5, 7,12,14,14,5, 11,6, 9
i. Calculate the mean of the sample?
ii. Calculate the variance of the sample?
iii. Calculate the standard deviation of the sample?
iv. Find the 95% confidence interval for the variance and standard deviation of the sample.
6. Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. Five hundred randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones.
i. Construct a 95% confidence interval for the proportion of adult residents of this city who have cell phones.
ii. Interpret the confidence interval found in part i.
7.You do a study of hypnotherapy to determine how effective it is in increasing the number of hours of sleep subjects get each night. You measure hours of sleep for 12 subjects with the following results. Construct a 95% confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data.
8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5

Answer 2

1. Describe the concept of statistics
2. Describe data
3. Describe variables
4. Analyze statistical problems using probabilities
5. Use sampling concepts in sampling procedures
6. Use statistical methods to test hypothesis
7. Estimate population parameters
8. Use statistical tests to interpret data

Answer 3

1.1 Definition of statistics
1.2 Statistic vs. statistics
1.3 Divisions of statistics
2.1 Types of data
2.2 Sources of data
2.3 Numerical presentation of data
2.4 Graphical and tabular presentation of data
2.5 Measurement scales
3.1 Types of variables
3.2 Measurement scales

Answer 4

.1 Definition of statistics
1.2 Statistic vs. statistics
1.3 Divisions of statistics
2.1 Types of data
2.2 Sources of data
2.3 Numerical presentation of data
2.4 Graphical and tabular presentation of data
2.5 Measurement scales
3.1 Types of variables
3.2 Measurement scales