Question

Mitchell works in the produce section at a small local supermarket and would like to test whether the proportion of apples people purchase is the same for each season, using a significance level of 0.025. He analyzes the apple purchases each season for a year and records his findings in the following table.

(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.)
TS =



(d) The test statistic follows a
chi-square distribution with df = 4
.


(e) Using the statistical table, the p-value is
0.01 < p-value < 0.025
.


(f) Based on the p-value, those conducting the test should
fail to reject
the null hypothesis at the significance level of 0.025.


(g) What is the appropriate conclusion?
There is sufficient evidence to conclude the distribution of apples purchased is not the same for each season.
There is sufficient evidence to conclude the total number of customers for each season are not all the same.
There is insufficient evidence to conclude the distribution of apples purchased is not the same for each season.
There is insufficient evidence to conclude the total number of customers for each season are not all the same.
There is sufficient evidence to conclude the distribution of customers apples purchased is the same for each season.

Answer 1

Mitchell conducted a hypothesis test to see if seasons affect apple purchases. The test statistic follows a chi-square distribution with df = 4, and the p-value suggests insufficient evidence to reject the null hypothesis, indicating apple purchases don't vary significantly by season.

Step-by-step explanation:

Mitchell wishes to determine if the proportion of apples purchased is the same for each season. To do this, he would perform a hypothesis test and calculate a test statistic (TS).

Although the value of TS is not provided, we understand that the test statistic follows a chi-square distribution with df = 4. With a given significance level of 0.025 and the statement that 0.01 < p-value < 0.025, the correct approach would be to fail to reject the null hypothesis.

Therefore, the appropriate conclusion would be that there is insufficient evidence to conclude that the distribution of apples purchased is not the same for each season.