Part A:
A restaurant wants to test a new in-store marketing scheme in a small number of stores before rolling it out nationwide. The new ad promotes a premium drink that they want to increase the sales of. 5 locations are chosen at random and the number of drinks sold are recorded for 2 months before the new ad campaign and 2 months after. The average difference in the sales quantity (after - before) is -42.749 with a standard deviation of 57.6675. Calculate a 90% confidence interval to estimate the true average difference in nationwide sales quantity before the ad campaign and after.
Part B
A suggestion is made that the proportion of people who have food allergies and/or sensitivities is 0.69. You believe that the proportion is actually different from 0.69. If you conduct a hypothesis test, what will the null and alternative hypothesis be?
| 1) | H_{O}: p ≥ 0.69 H_{A}: p < 0.69 | |
| 2) | H_{O}: p = 0.69 H_{A}: p ≠ 0.69 | |
| 3) | H_{O}: p ≠ 0.69 H_{A}: p = 0.69 | |
| 4) | H_{O}: p ≤ 0.69 H_{A}: p > 0.69 | |
| 5) | H_{O}: p > 0.69 H_{A}: p ≤ 0.69 | |
Part C
A suggestion is made that the proportion of people who have food allergies and/or sensitivities is 0.53. You believe that the proportion is actually different from 0.53. The hypotheses for this test are Null Hypothesis: p = 0.53, Alternative Hypothesis: p ≠ 0.53. If you select a random sample of 22 people and 11 have a food allergy and/or sensitivity, what is your test statistic and p-value?
| 1) | Test Statistic: 0.282, P-Value: 0.778 | |
| 2) | Test Statistic: -0.282, P-Value: 0.611 | |
| 3) | Test Statistic: -0.282, P-Value: 0.778 | |
| 4) | Test Statistic: -0.282, P-Value: 0.222 | |
| 5) | Test Statistic: -0.282, P-Value: 0.389 | |
Part D
Consumers Energy states that the average electric bill across the state is $103.08. You want to test the claim that the average bill amount is actually greater than $103.08. The hypotheses for this situation are as follows: Null Hypothesis: μ ≤ 103.08, Alternative Hypothesis: μ > 103.08. You complete a randomized survey throughout the state and perform a one-sample hypothesis test for the mean, which results in a p-value of 0.026. What is the appropriate conclusion? Conclude at the 5% level of significance.
| 1) | The true average electric bill is significantly different from $103.08. | |
| 2) | The true average electric bill is significantly less than $103.08. | |
| 3) | The true average electric bill is less than or equal to $103.08. | |
| 4) | We did not find enough evidence to say the true average electric bill is greater than $103.08. | |
| 5) | The true average electric bill is significantly greater than $103.08. | |