Answer to Question #195281 in Statistics and Probability for Thanu

Question

A study found that average Malaysians are making average monthly debt payments of

RM1200.                                                        

City Debt

George Town 1568

Kuala Lumpur 1385

Ipoh 1383

Kuching 1383

Putrajaya 830

a. Specify the population parameter to be tested. (1 Marks)

b. Specify the null and alternative hypotheses to test whether average monthly debt

payments are greater than RM1100. (2 Marks)

c. Calculate the sample mean debt payment and the sample standard deviation.

(2 Marks)

d. Compute the value of the appropriate test statistic. (2 Marks)

e. At the 10% significance level, calculate the p-value. (2 Marks)

f. At the 10% significance level, can we conclude that the average monthly debt payments

are greater than RM1200? (1 Mark)

Answer 1

(a) Population Parameters are-

$\mu=1200$

$\sigma=\sqrt{\dfrac{(x-\bar{x})^2}{n}}=\sqrt{\dfrac{313246.8}{5}}=\sqrt{62649.36}=250.29$

(b) NULL hypothesis$,H_o: \mu>RM1100$

Alternate Hypothesis, $H_a:\mu\le RM1100$

(c) Sample mean $\bar{x}=\dfrac{\sum x}{n}=\dfrac{6549}{5}=1309.8$

Sample standard deviation $s=\dfrac{\sigma }{\sqrt{n}}=\dfrac{250.29}{\sqrt{5}}=\dfrac{250.29}{2.236}=111.93$

(d) Test-Statistics is-

$t=\dfrac{x-\mu}{s}=\dfrac{1309.8-1200}{111.93}=\dfrac{109.8}{111.93}=0.9809$

(e)$\alpha=0.1,P(t>0.9809) =0.1633$ one tail t test at (n-1) i.e. 4 degree of freedom.

(f) As p-value is greater than $\alpha$ so we can't conclude that the average monthly debt payments

are greater than RM1200.