A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a random sample of 200 couples that had a child within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within five years. Use Scenario 8-4. A 90% confidence interval for the proportion p of all couples that had a child within the first two years of marriage and are divorced within five years is 0.402 ± 0.056.a. All the answers are correct.b. Based on this interval, we can clearly see that the divorce rate is well below the 50% national average for all marriages.c. At the 10% alpha level, we would reject the claim that the divorce rate is 50% for couples who had a child within the first two years of marriage.d. Based on this interval, we can clearly see that the divorce rate is between 35% and 46%.

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warylucknow warylucknow · Answer 1 · 2020-02-07T11:00:54+01:00

Answer:

The correct option is (a).

Step-by-step explanation:

The hypothesis of the study can be defined as:

H₀: The divorce rate is 50% for couples who had a child within the first two years of marriage, i.e. p = 0.50

Hₐ: The divorce rate is different from 50% for couples who had a child within the first two years of marriage, i.e. p ≠ 0.50

The 90% confidence interval is: 0.402 ± 0.056 = (0.346, 0.458) ≈ (0.35, 0.46)

The confidence level is 90%, the significance level (α) is:

[tex]\alpha =1-\frac{Confidence\ level}{100}\\=1-\frac{90}{100}\\ =0.10\ or\ 10\%[/tex]

Decision Rule:

If the null hypothesis value is not contained in the 90% confidence interval then the null hypothesis will be rejected and vice-versa.

Interpretation of the Confidence interval:

The confidence interval is (35%, 46%), this implies divorce rate is less than 50% for couples who had a child within the first two years of marriage.
At 10% significance level, the null hypothesis will be rejected stating that the divorce rate is different from 50% for couples who had a child within the first two years of marriage.
The confidence interval clearly interprets that 90% of the divorce rate for couples who had a child within the first two years of marriage is between 35% and 46%.

Thus all the options are correct.