Question

(1 point) Taste Test. Some people claim that they can tell the difference between a diet soda and a regular soda in the first sip. A researcher wanting to test this claim randomly sampled 124 such people. He then filled 124 plain white cups with soda, half diet and half regular through random assignment, and asked each person to take one sip from their cup and identify the soda as diet or regular. 83 participants correctly identified the soda. Round all answers to 4 decimal places.

1. What are the correct hypotheses for conducting a hypothesis test to determine if people are able to detect the difference between diet and regular soda, that is, is the proportion who choose correctly higher than what random guessing would predict?

A. ?0:?=0.5H0:p=0.5, ??:?<0.5HA:p<0.5
B. ?0:?=0.5H0:p=0.5, ??:?≠0.5HA:p≠0.5
C. ?0:?=0.5H0:p=0.5, ??:?>0.5HA:p>0.5

2. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.

4. Based on the p-value, we have:
A. very strong evidence
B. little evidence
C. some evidence
D. strong evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.

Answer 1

The statistical software output for this problem is :

Option B is correct.

Test statistics = 3.772

P-value = 0.000

Option A is correct .