Consider the following hypotheses: H0: = 410 HA: 410 The population is normally

Question

Consider the following hypotheses: H0: = 410 HA: 410 The population is normally distributed with a population standard deviation of 46. Use Table 1.

a. Use a 10% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

Critical value(s)?

± b- 1. Calculate the value of the test statistic with x-mean= 421 and n = 85. (Round your answer to 2 decimal places.)

Test statistic ?

b-2. What is the conclusion at = 0.10?

a)Do not reject H0 since the value of the test statistic is smaller than the critical value.

b)Do not reject H0 since the value of the test statistic is greater than the critical value.

c)Reject H0 since the value of the test statistic is smaller than the critical value.

d)Reject H0 since the value of the test statistic is greater than the critical value.

c. Use a 5% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

Critical value(s)?

d-1. Calculate the value of the test statistic x-mean= 397 and n = 85. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Test statistic ?

d-2. What is the conclusion at = 0.05?

a)Reject H0 since the value of the test statistic is not less than the negative critical value.

b)Reject H0 since the value of the test statistic is less than the negative critical value.

c)Do not reject H0 since the value of the test statistic is not less than the negative critical value.

d)Do not reject H0 since the value of the test statistic is less than the negative critical value.

Explanation / Answer

a-1) for it is two tailed test : critical value z =-/+ 1.64

b-1)

std error of mean =std deviaiton/(n)1/2 =4.9894

hence  Test statistic =(X-mean)/std deviation =(421-410)/4.9894=2.20

b-2)d)Reject H0 since the value of the test statistic is greater than the critical value.

c)

Critical value(s) = -/+1.96

d-1)

std error of mean =std deviaiton/(n)1/2 =4.9894

hence  Test statistic =(X-mean)/std deviation =(397-410)/4.9894=-2.61

d-2)

)Reject H0 since the value of the test statistic is less than the negative critical value.

please revert for any clarification required.

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