Question

Question 11 (1 point) Hypothesis Test. Do males wait longer to get married? In 1960, a study of 83 males showed the average age at which they first married was 23.3 years with a standard deviation of 4.9 years. Are men waiting longer to get married nowadays? Test at the .05 level of significance given that in 2019 a sample of 64 men was collected in which the average age at which they were first married was 24.2 years with a standard deviation of 5.3 years. Question. What is the correct statistical conclusion if the level of significance is 0.05? Reject the null hypothesis. Fail to reject the null hypothesis. Reject the alternate hypothesis. Accept the null hypothesis. None of these.

Answer 1

We have to test that men waiting longer to get married nowadays. We use Z-test for the equality of two means.

Hypothesis -

Null hypothesis - H₀ : Men waiting time for marriage today & in 1960 is equal. i.e.
11
=
112

Alternative hypothesis - H₁ : men waiting longer to get married nowadays. i.e.
11
>
112
.

Test statistic -

Ti- T2 N -2 2 + ni 112

Test criterion -

Reject H₀ if Z $\geq$ $Z_{\alpha}$.

Calculations -

Let, $\bar{x_{1}}$ be the sample mean of waiting time of men nowadays & $\bar{x_{2}}$ be the sample mean of waiting time of men in 1960.

So, $\bar{x_{1}}$ = 24.2, $\sigma_{1}$ = 5.3, n₁ = 64

$\bar{x_{2}}$ = 23.3, $\sigma_{2}$ = 4.9, n₂ = 83

So,

Ti- T2 N -2 2 + ni 112

$Z = \frac{24.2-23.3}{\sqrt{\frac{(5.3)^{2}}{64}+\frac{(4.9)^{2}}{83}}}$

$Z = \frac{0.9}{\sqrt{\frac{28.09}{64}+\frac{24.01}{83}}}$

$Z = \frac{0.9}{\sqrt{0.4389+0.2893}}$

$Z = \frac{0.9}{\sqrt{0.7282}}$

$Z = \frac{0.9}{0.8533}$

Critical value -

$Z_{\alpha}$ = Z_0.05 = 1.645

Conclusion -

Z (1.0457) < Z_$\alpha$ (1.645), So we fail to reject null hypothesis.

Option B is correct.