Question

Carl recorded the number of customers who visited his new store during the week:

Day	Customers
Monday	17
Tuesday	13
Wednesday	14
Thursday	16

He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)

What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.

Answer 1

To test the hypothesis is that the number of customers does not follow a uniform distribution at \(10 \%\) level of significance.

The null and alternative hypothesis is,

The null hypothesis is that the number of customers does follow a uniform distribution.

The alternative hypothesis is that the number of customers does not follow a uniform distribution.

The chi-square test statistic is,

By using MINITAB software, find chi-square with help of following steps:

1) Import the data.

2) Select Chi-Square Goodness-of-Fit Test (One Variable) from Tables in Stat menu.

3) Select Observed counts and Equal proportions.

4) \(\quad\) Click Ok.

From the MINITAB output, the chi-square test is \(0.67\)

The \(p\) -value is,

From the MINITAB output, the chi-square test \(p\) -value is \(0.881\).

Decision

The conclusion is that the significant \(p\) -value is greater than \(0.10\) which is \(0.881\), so the null hypothesis is not rejected at \(10 \%\) level of significance. There is insufficient evidence to indicate that the number of customers does not follow a uniform distribution. The result is not statistically significant.