Question

22. True or False Question The percentage of males in 1986 who are 18-19 years old and married was 3.7%. To test whether or not this percentage had increased in 2015, a random sample of 300 males aged 18-19 was taken; 20 of which were married. Using a level of significance of a = 0.05, we test the hypothesis H, that the proportion that is married is 3.7% against the alternative that it is larger. Based on the data, the observed value of the corresponding test statistic is 2.722 and we reject Ho. True False

Answer 1

Solution:

From the given information,

Test is right tailed or upper tailed test.

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 20

n = sample size = 300

p̂ = x/n = 20/300 = 0.066666667

p = 0.037

q = 1 - p = 0.963

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.066666667 - 0.037)/sqrt(0.037*0.963/300)

Z = 2.7222

Test statistic = Z = 2.722

Level of significance = α = 0.05

So, the critical Z value by using z-table is given as below:

Critical value = 1.645

Test statistic value is greater than critical value, so we reject the null hypothesis.

So, given statement is true.

Answer: True