# Part A: A restaurant wants to test a new in-store marketing scheme in a small number...

###### Question:

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.

 1) (-94.7165, 9.2185)
 2) (-68.5387, -16.9593)
 3) (-44.8808, -40.6172)
 4) (97.7287, 12.2307)
 5) (-97.7287, 12.2307)

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) HO: p ≥ 0.69 HA: p < 0.69
 2) HO: p = 0.69 HA: p ≠ 0.69
 3) HO: p ≠ 0.69 HA: p = 0.69
 4) HO: p ≤ 0.69 HA: p > 0.69
 5) HO: p > 0.69 HA: 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.
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