Question

Consider the following hypotheses:

H₀: μ = 9,100
H_A: μ ≠ 9,100

The population is normally distributed with a population standard deviation of 700. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can "reject/do not reject" the null hypothesis at the 10% significance level. (You may find it useful to reference the appropriate table: z table or t table) (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round "test statistic" values to 2 decimal places and "p-value" to 4 decimal places.)

		Test statistic	p-value
a.	x−x− = 9,190; n = 105			(Click to select)  Reject H0  Do not reject H0
b.	x−x− = 9,190; n = 255			(Click to select)  Reject H0  Do not reject H0
c.	x−x− = 8,830; n = 37			(Click to select)  Reject H0  Do not reject H0
d.	x−x− = 8,860; n = 37			(Click to select)  Do not reject H0  Reject H0

Answer 1

As population standard deviation is known, we will use z distribution to find the test statistics

a.

P value is

As P value greater than alpha=0.1, we fail to reject the null hypothesis

So Do not reject H0

b.

P value is

As P value is less than alpha=0.1, we reject the null hypothesis

So Reject H0

c.

P value is

As P value is less than alpha=0.1, we reject the null hypothesis

So Reject H0

d.

As P value is less than alpha=0.1, we reject the null hypothesis

So Reject H0