Question

Consider the following hypothesis test:

H ₀: u = 16

H _a: u ≠ 16

A sample of 50 provided a sample mean of 14.13. The population standard deviation is 3.

a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus “-“ sign.)

b. What is the p-value (to 4 decimals)?

c. Using  = .05, can it be concluded that the population mean is not equal to 16? (yes, no)

Answer the next three questions using the critical value approach.

d. Using  = .05, what are the critical values for the test statistic (to 2 decimals)? ± ______

e. State the rejection rule: Reject H ₀ if z is (greater than or equal to, greater than, less than or equal to, less than, equal to, not equal to) the lower critical value and is (greater than or equal to, greater than, less than or equal to, less than, equal to, not equal to) the upper critical value.

f. Can it be concluded that the population mean is not equal to 16?
(Yes, No)

Answer 1

Solution :

Given that,

Population mean = = 16

Sample mean = = 14.13

Population standard deviation = = 3

Sample size = n = 50

Level of significance = = 0.05

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 16

Ha: 16

a)

The test statistics,

Z =( - )/ (/)

= ( 14.13 - 16 ) / ( 3 /50)

= -4.41

b)

p-value = 2*P(Z < z )

= 2*P(Z < -4.41)

= 2* 0.0

= 0

c)

= 0.05

The p-value is p = 0, and since p = 0 < = 0.05, it is concluded that the null hypothesis is rejected.

Yes.  it be concluded that the population mean is not equal to 16

d)

Critical value

the critical value for a two-tailed test is

Z_{c = 1.96}

_e)

Since it is observed that |z| = 4.408 > Z_{c = 1.96}, it is then concluded that the null hypothesis is rejected.

f)

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population

mean μ is different than 16, at the 0.05 significance level.

Yes.  it be concluded that the population mean is not equal to 16.