Question

An organization surveyed 1040 adults in a certain country aged 18 and older and found that 538 believed they would not have enough money to live comfortably in retirement. Does the sample evidence suggest that a majority of adults in this country believe they will not have enough money in? retirement? Use the alpha equals 0.1 level of significance.

Answer 1

H0: p <= 0.5

Ha: p > 0.5 (Right tailed)

Sample proportion = 538 / 1040 = 0.5173

Test statistics

z = - p / sqrt(p(1-p)/n)

= 0.5173 - 0.5 / sqrt(0.5 * 0.5 / 1040 )

= 1.1158

This is test statistics value.

Critical value at 0.1 significance level is 1.2816

Since test statistics < 1.2816, we do not have sufficient evidence to reject H0.

We conclude at 0.1 level that we fail to support the claim that majority of adults in this

country believe they will not have enough money in retirement.