2 Consider the following hypotheses H0 u greater thanequal t

(2)

Consider the following hypotheses:

H0: u greater than/equal to 204

HA: u < 204

A sample of 76 observations results in a sample mean of 188. The population standard deviation is known to be 16. Use Table 1.

a.

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

Critical Value
a = 0.10   
a = 0.01   

b-1.

Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

  Test statistic   

b-2.

Does the above sample evidence enable us to do not reject the null hypothesis at a = 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 do not reject the null hypothesis at a = 0.01?

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.

Solution

a) Critical Value
a = 0.10 , za = -1.28
a = 0.01, za = -2.33

b-1.Test statistic =(188-204)/(16/SQRT(76)) = -8.72

b-2. No since the value of the test statistic is less than the negative critical value.

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