Question

An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A sample of 234 fathers from Littleton yielded 96 who did not help with child care. Use the critical value method to test the researcher's claim at the 0.05 significance level. Does the article report need to be corrected?

1. State the requirement
2. State the null and alternative hypotheses with the correct symbols
3. Write all the statistics
4. Write the formula of the test statistic and find the test statistic (you may use a calculator, but you are required to write down the command and all the numbers you enter)
5. Find the critical value or the P-value (you may use a calculator, but you are required to write down the command and all the numbers you enter)
6. Decide to reject or fail to reject H₀ and explain the reason
7. Wording the conclusion
8. Answer the question based on your result above

Answer 1

Solution :

This is the right  tailed test .

The null and alternative hypothesis is

H0 : p = 0.34

Ha : p > 0.34

= x / n = 96/234 = 0.4103

P0 = 0.34

1 - P0 = 1 -0.34 = 0.66

= 0.05

The critical value for a right-tailed test is zc​=1.645

The rejection region for this right-tailed test is z >1.645

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.4103- 0.34 / [0.34*(0.66) /234 ]

= 2.269

P(z > 2.269) = 1 - P(z < 2.269) = 0.0116

P-value = 0.0116

= 0.05

0.0116< 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that figure is higher for fathers in the town of Littleton.

The article report need to be corrected