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) 0.0015
B) 0.0038
C) 0.0529
D) 0.0019

Question

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)  0.0015 
B)  0.0038 
C)  0.0529 
D)  0.0019

Quizplus · Accepted Answer

To find the P-value for the hypothesis test, we first need to determine the test statistic and then use it to find the P-value. The null hypothesis (H0) is that the proportion of fathers in Littleton who do not help with child care is 34% (0.34), and the alternative hypothesis (Ha) is that the proportion is higher than 34%.1. Calculate the sample proportion (p̂): p̂ = 97/225 = 0.43112. Calculate the test statistic using the formula for a one-sample z-test for proportions: z = (p̂ - p0) / sqrt(p0(1-p0)/n), where p0 = 0.34, n = 225.   z = (0.4311 - 0.34) / sqrt(0.34 * 0.66 / 225) ≈ 3.273. The P-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. Since this is a one-tailed test (the claim is that the figure is higher), we find the area to the right of z = 3.27 in the standard normal distribution.Using a standard normal distribution table or calculator, the P-value associated with z = 3.27 is approximately 0.0019. This means there is a very small probability of observing a sample proportion as extreme as 0.4311 if the true population proportion is 0.34, supporting the researcher's claim that the figure is higher for fathers in Littleton.

Find the P -Value for the Indicated Hypothesis Test