Question

are phone calls equally likely to occur any day of the week? the day of the week for each of 588 randomly selected phone calls was observed. the results are displayed in the table below. use an $\alpha =$ 0.05 significance level.
a. complete the rest of the table by filling in the expected frequencies:
frequencies of phone calls for each day of
the week
b. what is the correct statistical test to use?
select an answer
c. what are the null and alternative hypotheses?
$h_0$:
the distribution of phone calls is not uniform over the days of the week.
phone calls and days of the week are dependent.
the distribution of phone calls is uniform over the days of the week.
phone calls and days of the week are independent.

Explanation:

Part a

Step1: Calculate total calls

Total calls = 91 + 80 + 69 + 102 + 87 + 77 + 82 = 588

Step2: Compute expected frequency

Expected frequency = Total calls / 7 = 588 / 7 = 84

Part b

The problem tests if phone calls are uniformly distributed over days of the week, which requires a goodness-of-fit test for uniform distribution.

The null hypothesis ($H_0$) for uniform distribution states the distribution is uniform; the alternative ($H_1$) states it is not.

Answer:

Chi-square goodness-of-fit test

Part c