Question

The mean waiting time at the​ drive-through of a​ fast-food restaurant from the time an order is placed to the time the order is received is 85.5 seconds. A manager devises a new​ drive-through system that he believes will decrease wait time. As a​ test,he initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts​ (a) and​ (b) below.

109.0
66.8
58.4
74.6
67.4
81.4
95.5
84.7
70.9
81.3

b) Is the new system​ effective? Conduct a hypothesis test using the​ P-value approach and a level of significance of

alpha equals 0.05α=0.05.

First determine the appropriate hypotheses.

Upper H 0H0​:

Upper H 1H1​:

Find the test statistic.

t 0t0equals=nothing

​(Round to two decimal places as​ needed.)

Find the​ P-value.

The​ P-value is?

​(Round to three decimal places as​ needed.)

Use the

alpha equals α=0.05 level of significance.

What can be concluded from the hypothesis​ test?

A.The​ P-value is

greatergreater

than the level of significance so there

isnbsp not nbsp not sufficient

evidence to conclude the new system is effective.

B.The​ P-value is

lessless

than the level of significance so there

isnbsp not nbsp not sufficient

evidence to conclude the new system is effective.

C.The​ P-value is

greatergreater

than the level of significance so there

isnbsp sufficient

evidence to conclude the new system is effective.

D.The​ P-value is

lessless

than the level of significance so there

isnbsp sufficient

evidence to conclude the new system is effective.

Answer 1

Here in this scenario the managers claim is that a new​ drive-through system will decrease wait time from 85.5 second.

To test this claim we have to use one sample t test because here the population standard deviations is unknown and sample size is less than 30.

Before performing test we have to calculate the sample mean and standard deviations as below,

The sample mean is 79 and sample Standerd deviation

s= 14.9388.

Further the test is performed at 0.05 level of significance as below,

The t critical value is calculated using t table at left tailed and 9 degrees of freedom.

First determine the appropriate hypotheses.

Upper H0: The mean wait time order received is 85.5 sec.

Upper H1:The mean wait time order received is less than 85.5.

Find the test statistic.

t0 = -1.38

​(Rounded to two decimal places as​ needed.)

The P-value.

The​ P-value is 0.101

​(Rounded to three decimal places as​ needed.)

Using

alpha equals α=0.05 level of significance.

Conclusion : since p value is greater than alpha level of significance 0.101>0.05 so we fail to Reject Ho null hypothesis and concluded that there is not enough evidence to support claim that the mean waiting time to order received is less than 85.5.

Option A is correct.

A.The​ P-value is

greatergreater

than the level of significance so there

isnbsp not nbsp not sufficient

evidence to conclude the new system is effective

Hope you understood.

Thank you.