Question

Consider the following hypothesis test.

H0: μ = 15

Ha: μ ≠ 15

A sample of 50 provided a sample mean of 14.08. The population standard deviation is 3.

A. Find the value of the test statistic. (Round your answer to two decimal places.)

B. Find the p-value. (Round your answer to four decimal places.)

C. State the critical values for the rejection rule. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

Answer 1

Solution :

= 15

=14.08

=3

n = 50

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 15

Ha :     15

a ) Test statistic = z

= ( - ) / / n

= (14.08 -15 ) / 3 / 50

= −2.168

Test statistic = z =  −2.17

b ) P(z >-2.17 ) = 1 - P(z < -2.17 ) = 1 - 0.985

P-value = 2 * 0.0150 = 0.0300

c ) It is observed that ∣z∣=2.168>zc​=1.96, it is then concluded that the null hypothesis is rejected.