Question

Consider the following hypothesis test: Ho: u = 15 Hai ji #15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 4. Enter negative value as negative number. a. Compute the value of the test statistic (to 2 decimals). -.03 b. What is the p-value (to 4 decimals)? Use the value of the test statistic rounded to 2 decimal places in your calculations. c. Using a = 0.05, can it be concluded that the population mean is not equal to 15? - Select your answer - A Answer the next three questions using the critical value approach. d. Using a = 0.05, what are the critical values for the test statistic? (+ or -) (to 2 decimals) the lower critical value and is - Select your answer - the upper critical value. State the rejection rule: Reject Ho if z is - Select your answer Can it be concluded that the population mean is not equal to 15? - Select your answer - 4

Answer 1

Part a)

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 14.15 - 15 ) / ( 4 / √( 50 ))
Z = -1.50

Part b)

P value = 2 * P ( Z > 1.50 ) = 2 * 1 - P ( Z < 1.50 ) = 0.1329

Looking for the value Z = 1.50 in standard normal table to find the P value

Part c)

Decision based on P value
Reject null hypothesis if P value < α = 0.05 level of significance
Since 0.1329 > 0.05, hence we fail to reject null hypothesis
Result :- We fail to reject null hypothesis

Part d)

Critical value Z(α/2) = Z( 0.05 /2 ) = ± 1.96

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 ) i.e Z < -1.96 OR Z > 1.96
| Z | > Z( α/2 ) = 1.50 < 1.96
Result :- Fail to reject null hypothesis

State the rejection rule: Reject Ho if z is - Select your answer - 4 the lower critical value and is - Select your answer - 4 the upper critical value.

Reject null hypothesis if   Z < -1.96 OR Z > 1.96