Question

Question 4 (6 marks) Part a) Calculate the statistic, set up the rejection region, interpret the result, and draw the sampling distribution. Ho: Hi: μ 10 μ#10 Given that: σ-10, n-100, X-10, α-0.05. Part b) A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as X -175 and s-22. Calculate the value of the test statistic of the test required to determine whether there is enough evidence to infer at the 5% significance level that the population mean is different from 180.

Answer 1

Part (a)

SE = /

= 10/= 1

Test statistic is:
Z = (10 - 10)/1 =0

(i)

The statistic is:

Z = 0

(ii)

= 0.05

From Table, critical values of Z = 1.96

Rejection Region:
Reject H0 if:

Z < - 1.96

OR

Z > 1.96

(iii)

Since the calculated value of Z =0 is not in the Rejection Region, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that the population mean is different from 10.

(iv) The Sapling Distribution of Sample mean is Normal Distribution with mean = population mean = = 10 and Standard Deviation = SE =1.

Part (b):

SE = s/

= 22/= 1.5556

V200

Test statistic is:
t = (175 - 180)/1.5556 = - 3.2141

(i)

The statistic is:

t = - 3.2141

(ii)

= 0.05

ndf = 200 - 1 = 199

From Table, critical values of t = 1.9720

Rejection Region:
Reject H0 if:

Z < - 1.9720

OR

Z > 1.9720

(iii)

Since the calculated value of Z = - 3.2141 is in the Rejection Region, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the population mean is different from 180.