Question

question 24
not yet
answered
points out of
1.00
flag question
pizza hut advertises that all pizza deliveries will take 40 minutes or less from the time an order
is placed. one frustrated customer thinks that the average delivery time is more than 40
minutes. the customer takes a simple random survey of 16 customers and finds that the
average length of delivery was 44 minutes, and the standard deviation of the sample is 7
minutes. a hypothesis test is done at the 0.01 level of significance.
what is the alternative hypothesis?
question 25
not yet
answered
points out of
1.00
flag question
find the critical value. keep in mind, you do not know the population standard deviation.
answer:
question 26
not yet
answered
points out of
1.00
flag question
find the value of the test statistic. round your answer to three decimal places.
answer:
question 27
not yet
answered
points out of
1.00
flag question
make a conclusion.

Explanation:

Question 24

The customer thinks the average delivery time is more than 40 minutes. In hypothesis testing, the alternative hypothesis \(H_{1}\) represents the claim we are trying to find evidence for. If the null hypothesis \(H_{0}:\mu = 40\), then the alternative hypothesis for "more than" is \(H_{1}:\mu>40\).

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 16\). So \(df=16-1 = 15\).

Step2: Find the critical value for a one - tailed test (\(\alpha=0.01\))

Using the t - distribution table (one - tailed), for \(df = 15\) and \(\alpha=0.01\), the critical value \(t_{\alpha,df}=t_{0.01,15}=2.602\)

Step1: Recall the formula for the t - test statistic

The formula for the t - test statistic is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\), where \(\bar{x}=44\), \(\mu = 40\), \(s = 7\), and \(n = 16\)

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Answer:

a. \(\mu > 40\)

Question 25