Question

Suppose that you are examining the difference in ages between brides and grooms. You are interested in conducting a significance test to examine to address the theory that the bride is younger than the groom in more than half of all marriages. A sample of 100 couples were observed, for which 67 had a bride younger than the groom.

whats is the parameter? .

Step 2: The null hypothesis and alternative hypothesis?

Step 5: whats the  p-value is:

Answer 1

Solution:

Here, we have to use one sample z test for the population proportion.

What is the parameter?

The parameter for this test is given as the population proportion that the bride is younger than the groom in more than half of all marriages.

Step 2: The null hypothesis and alternative hypothesis?

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: the bride is not younger than the groom in more than half of all marriages.

Alternative hypothesis: Ha: the bride is younger than the groom in more than half of all marriages.

H0: p = 0.5 versus Ha: p > 0.5

This is an upper tailed test.

We are given

Level of significance = α = 0.05

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 = 67

n = sample size = 100

p̂ = x/n = 67/100 = 0.67

p = 0.50

q = 1 - p = 0.50

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.67 - 0.50)/sqrt(0.50*0.50/100)

Z = 3.40

Test statistic = 3.40

Step 5: what the p-value is:

P-value = 0.0003

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the bride is younger than the groom in more than half of all marriages.