After gathering data from a random sample of 32 sellers of propane, a 95% confidence interval for the mean price of a gallon of propone in the state of Georgia was found to be $2.60 to $2.78.

Question

According to the confidence interval which one of the following statements should we disputed?

Question 21 options:

The mean price for a gallon of propane in the state of Georgia is $2.75

The mean price for a gallon of propane in the state of Georgia is $2.62

The mean price for a gallon of propane in the state of Georgia is $2.69

The mean price for a gallon of propane in the state of Georgia is $2.85

Question 22 (1 point)

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This scatterplot shows variables with an association that is best described as...

Question 22 options:

positive and linear

positive and non-linear

negative and linear

negative and non-linear

Question 23 (1 point)

When the p-value from a hypothesis test is very small (less than the level of significance), this is an indication that ...

Question 23 options:

a type I error will likely occur

a type II error will likely occur

there is not enough evidence to claim the alternative hypothesis appears to be true

there is strong evidence to claim the alternative hypothesis appears to be true

Question 24 (1 point)

A person claims that more than 40% of people filing their tax forms in April will be getting a refund on their federal taxes. The null and alternative hypotheses for this claim are:

Ho: p = 0.40 and Ha: p > 0.40

From a random sample of 400 people filing their tax forms in April, it was determined that 168 will be getting a refund on their federal taxes. What is the p-value for this test?

Question 24 options:

0.414

0.207

0.816

0.793

Question 25 (1 point)

A hypothesis test for Ho: p = 0.80 vs. Ha: p < 0.80 was conducted and the p-value was found to be 0.17. If the test was using a level of significance of 0.05, then we should....

Question 25 options:

reject the null hypothesis

fail to reject the null hypothesis

not make a decision as we do not have enough information

none of the above

Answer 1

Let’s go through the questions one by one:

Question 21

The confidence interval for the mean price of a gallon of propane in Georgia is $2.60 to $2.78. To determine which statement should be disputed, we consider values outside the confidence interval:

• The mean price for a gallon of propane in Georgia is $2.75 → This value is inside the interval (disputed).
• The mean price for a gallon of propane in Georgia is $2.62 → This value is inside the interval (not disputed).
• The mean price for a gallon of propane in Georgia is $2.69 → This value is inside the interval (not disputed).
• The mean price for a gallon of propane in Georgia is $2.85 → This value is outside the interval (this value should be disputed).

Answer: The mean price for a gallon of propane in the state of Georgia is $2.85.

Question 22

Without the scatterplot, it’s impossible to determine the association. However, to choose the correct option, you might consider the general characteristics of scatterplots:

• If points tend to rise together from left to right, it's positive and linear.
• If points rise but curve up, it's positive and non-linear.
• If points tend to fall together, it's negative and linear.
• If points fall but curve down, it's negative and non-linear.

Without seeing the scatterplot, I cannot provide a final answer. Please evaluate the scatterplot with these descriptions.

Question 23

When the p-value from a hypothesis test is very small (less than the level of significance), it suggests strong evidence against the null hypothesis. This means we have evidence that supports the alternative hypothesis.

Answer: there is strong evidence to claim the alternative hypothesis appears to be true.

Question 24

To calculate the p-value for the given hypotheses \( H_0: p = 0.40 \) and \( H_a: p > 0.40 \).

The sample proportion \( \hat{p} = \frac{168}{400} = 0.42 \).

Using the standard formula for the z-test:

1. Compute the standard error (SE): \[ SE = \sqrt{\frac{p_0(1 - p_0)}{n}} = \sqrt{\frac{0.40(0.60)}{400}} = \sqrt{\frac{0.24}{400}} = \sqrt{0.0006} \approx 0.02449 \]
2. Compute the z-score: \[ z = \frac{\hat{p} - p_0}{SE} = \frac{0.42 - 0.40}{0.02449} \approx \frac{0.02}{0.02449} \approx 0.817 \]
3. Determine the p-value from the z-score associated with the standard normal distribution.

Using a z-table, the p-value corresponding to \( z = 0.817 \) is approximately 0.207.

Answer: 0.207

Question 25

With a p-value of 0.17 and a significance level of 0.05, since the p-value is greater than the level of significance, we fail to reject the null hypothesis.

Answer: fail to reject the null hypothesis.