Question

Factinate claims that 84% of teenagers think highly of their mother. To investigate this claim, a school psychologist selects a random sample of 150 teenagers and finds that 135 think highly of their mother. Do these data provide convincing evidence that the true proportion of teens who think highly of their mother is greater than 0.84?
1. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest The school psychologist performed the significance test and obtained a P-value of 0.0225.
2. Explain what it would mean for the null hypothesis to be true in this setting.
3. Interpret the P-value.
4. What conclusion would you make at the a = 0.05 level?

Answer 1

Use the z-distribution, we have that:

1.

The null hypothesis is of $H_0: p = 0.84$.

The alternative hypothesis is of $H_1: p > 0.84$.

2. It would mean that at most 84% of teenagers think highly of their mother, as we could not conclude that the proportion is more than 84%.

3. We are working with a right-tailed test, hence it means that there is a 0.0225 = 2.25% probability that at least 0.9 = 90% of teenagers think highly of their mother.

4. The p-value is of 0.0225, which is less than the significance level of 0.05, which means that we would reject the null hypothesis.

How the p-value influences the decision?

• If the p-value is less than the significance level, the null hypothesis is rejected.

• If the p-value is more than the significance level, the null hypothesis is not rejected.

Item 1:

At the null hypothesis, we test if the proportion of teenagers that think highly of their mother is of 84%, hence:

$H_0: p = 0.84$

At the alternative hypothesis, we test if this proportion is greater than 84%, that is:

$H_1: p > 0.84$

Item 2:

It would mean that at most 84% of teenagers think highly of their mother, as we could not conclude that the proportion is more than 84%.

Item 3:

135/150 = 0.9.

We are working with a right-tailed test, hence it means that there is a 0.0225 = 2.25% probability that at least 0.9 = 90% of teenagers think highly of their mother.

Item 4:

The p-value is of 0.0225, which is less than the significance level of 0.05, which means that we would reject the null hypothesis.

More can be learned about the use of the z-distribution for an hypothesis test at https://brainly.com/question/26454209