Find the P-value for the indicated hypothesis test.
-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 random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Find the P-value for a test of the researcher's claim.
A)0.0529
B)0.0019
C)0.0015
D)0.0038

Question

Quizplus · Accepted Answer

To find the P-value for the hypothesis test, we first need to determine if the sample proportion of fathers in Littleton who do not help with child care is significantly higher than the reported 34%. The sample proportion is 97 out of 225, which is 97/225 = 0.4311 or 43.11%. To test the researcher's claim that this proportion is higher, we use a one-tailed test.The null hypothesis (H0) is that the proportion of fathers in Littleton who do not help with child care is 34% (p0 = 0.34), and the alternative hypothesis (Ha) is that the proportion is higher than 34%.Using the sample proportion (p = 0.4311), the sample size (n = 225), and the population proportion under the null hypothesis (p0 = 0.34), we calculate the test statistic. However, the exact calculation of the test statistic and the subsequent P-value is not shown here. The correct P-value for this scenario, given the options, is 0.0019, which indicates that there is a very low probability of observing a sample proportion as extreme as 43.11% if the true proportion were really 34%. This suggests that the researcher's claim that the figure is higher in Littleton is supported by the sample data.

Find the P-Value for the Indicated Hypothesis Test