Question

A large furniture store has begun a new ad campaign on local television. Before the campaign, the long-term average daily sales were $24,819. A random sample of 40 days during the new ad campaign gave a sample mean daily sale average of = $25,910. Does this indicate that the population mean daily sales are now more than $24,819? Use a 1% level of significance. Assume σ = $2159. Based on the calculated P-value will you reject or fail to reject the null hypothesis?

Select one:

a. reject the null hypothesis / data is significant

b. fail to reject the null hypothesis

c. cannot be determined

Interpret your conclusion in the context of the problem.

Select one:

a. At the 1% level of significance, data is sufficient to conclude that the long-term daily average sales is now greater than $24,819.

b. At the 1% level of significance, data is insufficient to conclude that the long-term daily average sales is now greater than $24,819.

c. At the 1% level of significance, data is sufficient to conclude that the long-term daily average sales is different than $24,819.

d. At the 1% level of significance, data is insufficient to conclude that the long-term daily average sales is now less than $24,819.

Answer 1

Here we have given that,

Claim: To check whether the population mean daily sales are more than $24819 .

The Hypothesis is as follows

v/s

We have given that,

n= Number of observation = 40

= sample mean =$ 25910

and we assume that

= population standard deviation =$ 2159

Now, we can find the test statistic

= 3.20

we get,

the Test statistic is 3.20

Now we find the P-value

= level of significance=0.01

This is one Right tailed test

Now, we can find the P-value

P-value =(P(Z > z)

=[1- P( Z < 3.20) ]

= [ 1 - 0.9993 ] using standard normal z probability table

= 0.0007

we get the P-value is 0.0007

Decision:

P-value < 0.01 ()

That is we reject Ho (Null Hypothesis) / data is significant

that is here option A is correct.

Conclusion:

There is the sufficient evidence that the population mean daily sales are more than $24819

At the 1% level of significance, data is sufficient to conclude that the long-term daily average sales is now greater than $24,819.

That is here option A is correct.