You draw a simple random sample of 25 businesses in Milwaukee and ask them how many hours per day they were open this past Memorial Day. Assume each individual draw is normally distributed with a standard deviation of 2. In your sample, businesses were open an average of 8.5 hours. Using a 4% significance level, you wish to test whether the population mean is 9 hours. Calculate the relevant test statistic for this test. If necessary, round your answer to four decimal places.

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mtosi17 mtosi17 · Answer 1 · 2020-06-27T02:06:24+02:00

Answer:

There is not enough evidence to support the claim that the population mean is significantly different from 9 hours.

Test statistic z = -1.25

P-value = 0.2113

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean is significantly different from 9 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=9\\\\H_a:\mu\neq 9[/tex]

The significance level is 0.04.

The sample has a size n=25.

The sample mean is M=8.5.

The standard deviation of the population is assumed to be known and has a value of σ=2.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{2}{\sqrt{25}}=0.4[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{8.5-9}{0.4}=\dfrac{-0.5}{0.4}=-1.25[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=2\cdot P(z<-1.25)=0.2113[/tex]

As the P-value (0.2113) is bigger than the significance level (0.04), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the population mean is significantly different from 9 hours.