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SVEN [57.7K]
3 years ago
12

Ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute in

dicate that the percentage is now 44%. (a) Choose the appropriate hypotheses such that rejection of H0 will support the conclusion that a smaller proportion of American families own stocks or stock funds this year than 10 years ago. H0: p - Select your answer - Ha: p - Select your answer - (b) Assume the Investment Company Institute sampled 300 American familie
Mathematics
1 answer:
stiks02 [169]3 years ago
3 0

Answer:

a) The null and alternative hypothesis are:

H_0: \pi=0.53\\\\H_a:\pi

b) If 300 families were sampled, for a significance level of 5%, there is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago (P-value = 0.001).

 

Step-by-step explanation:

The claim that we want to have evidence to support is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

The hypothesis for this test should state:

- For the null hypothesis, that the population proportion is not significantly different from 53%.

H_0:\pi=0.53

- For the alternative hypothesis, that the population proportion is significantly less than 53%.

H_a: \pi

If 300 families are sampled, we can perform a hypothesis test for a proportion.

The claim is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

Then, the null and alternative hypothesis are:

H_0: \pi=0.53\\\\H_a:\pi

The significance level is 0.05.

The sample has a size n=300.

The sample proportion is p=0.44.

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.53*0.47}{300}}\\\\\\ \sigma_p=\sqrt{0.00083}=0.029

Then, we can calculate the z-statistic as:

z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.44-0.53+0.5/300}{0.029}=\dfrac{-0.088}{0.029}=-3.065

This test is a left-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z

As the P-value (0.001) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

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