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 random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Using a .05 level of significance test the claim that the proportion is at least 34%.

State the null hypothesis H0: _____________

State the alternative hypothesis H1: _____________

What is the test statistic used for the test (z or t)

State the significance or alpha (?) level

Determine the p-value.

Do you or do you not reject the null hypothesis? Why?

Write a clear conclusion using a complete sentence.

Answer 1

Solution:

Claim: Proportion of American fathers take no responsibility for child care is at least 34%

Let p represent proportion of population of Amercian fathers take no responsibility for child care

p₀=0.34

Null Hypothesis: H₀: p=p₀

Alternative Hypotheis : H₁:

Sample size 225 which is more than 30 so Z test statistic can be used

Z test statistic is used

test statistic is

Here,

n=225

= Proportion of American fathers take no responsibility for child care of random sample = = 0.43

  

  

z= 2.81

p-value for 2.81 at 0.05 level of significance 0.00024 <0.05

Hence , it reject the null hypothesis

The claim that proportion is at least 34% is correct.