Consider the following hypotheses H0 380 HA 380 The populat

Consider the following hypotheses: H0: = 380 HA: 380 The population is normally distributed with a population standard deviation of 80. Use Table 1.

a. Use a 1% 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 1formula287.mml = 414 and n = 40. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.) Test statistic

b-2. What is the conclusion at = 0.01?

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

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

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

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

c. 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) ±

d-1. Calculate the value of the test statistic with 1formula287.mml = 351 and n = 40. (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

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

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

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

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

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

Solution

a) critical value = ± 2.58
(b)1) test statistic= sqrt(40) * (414 - 380 ) / 80 = 2.69
b-2) reject H0 as test statistic > critical value!
c) Critical value for 10% level of significance = ± 1.64

d) test statistic = sqrt(40) * ( 351- 380 ) / 80 = - 2.29

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