Question

1) A nation fast food chain claims that the waiting time of customers for service is normally distributed with a mean of 3 minutes or less. a) State the Hypothesis to show conclude the average waiting time for service is less than 3 minutes. b) Choose a level of a. Use a = 0.05 for this problem. c) To test the hypothesis, you take a sample of 50 customers and records the wait time. The data appear in the Waiting Time worksheet of the HW1 data workbook on Moodle. Collect data and calculate necessary statistics to test the hypothesis. d) Sketch the sampling distribution. Include the critical value and test statistic e) Draw a conclusion and report that in the problem context.

3.7
3.0
2.0
4.3
2.5
4.2
2.0
4.3
1.8
3.4
1.7
2.5
1.4
2.6
2.4
3.4
3.7
3.9
3.0
1.7
3.1
1.2
2.1
3.1
3.1
1.4
3.4
1.6
4.5
3.3
3.6
2.1
2.2
1.0
2.7
2.1
1.1
4.3
4.7
2.8
2.5
3.7
2.9
2.5
3.1
2.7
1.0
3.6
3.4
1.2

Please do all especially excel for c!

Answer 1

Part (a)

Let $\mu$ be the population mean waiting time.

to test, $H_0: \mu=3 \ vs. \ H_1:\mu\leq 3$ at $\alpha = 0.05$ level of significance.

The test statistic is given by,

SIVn

Under null hypothesis, $t \sim t_{n-1}$
where, $\overline{X}$ is the mean of the sample of 50 observations, $\mu_0 =3$, $s$ is the sample standard deviation and n = 50

The value of the test statistic is obtained as, t = -1.7658

the critical value is given as $-t_{0.05;49} = -1.6765$

Since observed t statistic < critical value for the lower tailed test, we shall reject the null hypothesis, thus stating that mean waiting time is less than 3 minutes.

The sampling distribution is sketched as follows,

The first tick is the test statistic and the second tick is the lower critical value.

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