Home / AP® Exam / AP® Statistics / 8.1 Introducing Statistics: Are My Results Unexpected? – MCQs

AP Statistics 8.1 Introducing Statistics: Are My Results Unexpected? - MCQs - Exam Style Questions

AP Statistics -MCQs and Answers - All Topics

Question

The table below shows historical data for the distribution of the number of customers, in half-hour time periods, who visit the electronics department of a retail store. For example, in \(25\) percent of the time periods for which data were collected, no customers were observed in the electronics department of the store.
Number of customers\(0\)\(1\)\(2\)\(3\) or more
Proportion of time periods\(0.25\)\(0.20\)\(0.30\)\(0.25\)
To investigate if the distribution has changed, the number of customers who visited the electronics department of the store was recorded for each of \(50\) randomly selected time periods. The results are shown in the table below.
Number of customers\(0\)\(1\)\(2\)\(3\) or more
Number of time periods\(4\)\(13\)\(14\)\(19\)
A chi-square goodness-of-fit test was conducted to determine whether the data provide convincing evidence that the distribution has changed. The test statistic was \(10.13\) with a p-value of \(0.0175\). Which of the following statements is true?
(A) At the significance level \(\alpha=0.05\), the data provide convincing evidence that the current distribution is different from the historical distribution.
(B) At the significance level \(\alpha=0.10\) the data do not provide convincing evidence that the current distribution is different from the historical distribution.
(C) The mean number of customers in a randomly selected time period is \(12.5\).
(D) No valid conclusion can be made because the observed frequency for one cell is less than \(5\).
(E) The chi-square statistic has \(50-1=49\) degrees of freedom.
▶️ Answer/Explanation
Detailed solution

1. State the Conclusion Rule:
If the p-value is less than or equal to the significance level (\(\alpha\)), we reject the null hypothesis and conclude there is convincing evidence for the alternative.

2. Analyze the Hypotheses:
– \(H_0\): The current distribution is the same as the historical distribution.
– \(H_a\): The current distribution is different from the historical distribution.

3. Compare p-value to \(\alpha\):
– The given p-value is \(0.0175\).
– The significance level in option (A) is \(\alpha = 0.05\).
– Since \(0.0175 < 0.05\), we reject \(H_0\). This means the data provide convincing evidence that the distribution has changed.
✅ Answer: (A)

More AP Statistics MCQ Questions..
Scroll to Top