Question

(Round all intermediate calculations to at least 4 decimal places.) Consider the following hypotheses: H0: μ =208 HA: μ < 208 A sample of 74 observations results in a sample mean of 202. The population standard deviation is known to be 26. Use Table 1

a. What is the critical value for the test with α = 0.10 and with α = 0.01? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Critical Value α = 0.10 α = 0.01

b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Test statistic

b-2. Does the above sample evidence enable us to reject the null hypothesis at α = 0.10?

Yes since the value of the test statistic is less than the negative critical value.

No since the value of the test statistic is not less than the negative critical value.

Yes since the value of the test statistic is not less than the negative critical value.

No since the value of the test statistic is less than the negative critical value

c. Does the above sample evidence enable us to reject the null hypothesis at α = 0.01?

No since the value of the test statistic is not less than the negative critical value.

Yes since the value of the test statistic is less than the negative critical value.

Yes since the value of the test statistic is not less than the negative critical value.

No since the value of the test statistic is less than the negative critical value.

Answer 1

Ans:

H₀: μ =208

H_A: μ < 208

n=74

Sample mean=202

population standard deviation= 26

a)

For alpha=0.1,

critical z value=-1.28

For alpha=0.01

critical z value=-2.33

b)

Test statistic:

z=(202-208)/(26/sqrt(74))

z=-1.99

c)As,test statistic,z=-1.99 is less than critical z value -1.28,we reject the null hypothesis.

Yes since the value of the test statistic is less than the negative critical value.

d)As,test statistic,z=-1.99 is not less than critical z value -2.33,we do not reject the null hypothesis.

No since the value of the test statistic is not less than the negative critical value.