Mathematics, 05.07.2020 14:01, tylerjoshonti

Researchers conducted a study to find out if there is a difference in the use of eReaders by different age groups. Randomly selected participants were divided into two age groups. In the 16- to 29-year-old group, 7% of the 627 surveyed use eReaders, while 11% of the 2,314 participants 30 years old and older use eReaders. Use a = 0.05. Required:a. State the null hypothesis. b. State the alternative hypothesis. c. State the distribution to use for the test. (Round your answers to four decimal places.) d. Determine the test statistic using your data. (Round your answers to two decimal places.) e. What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. f. Draw a graph and label it appropriately. Shade the actual level of significance. g. Do you or do you not reject the null hypothesis? Why? h. Write a clear conclusion using a complete sentence.

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answered: jwyapo4

a+b) The null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

c) Distribution: standard normal distribution.

d) Test statistic z = -2.9398.

e) P-value = 0.0033.

This P-value shows the probability of having this outcome (sample results) given that the null hypothesis is true (that there is no difference in the proportions). This low value of the P-value shows that is unlikely that this results is only due to chance, so it works as evidence against the null hypothesis.

f) Attached.

The null hypothesis is rejected, as the P-value is smaller than the significance level.

There is enough evidence to support the claim that there is a significant difference in the use of eReaders by different age groups.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is a significant difference in the use of eReaders by different age groups.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1 (16-29 years old), of size n1=627 has a proportion of p1=0.07.

The sample 2 (30+ years old), of size n2=2314 has a proportion of p2=0.11.

The difference between proportions is (p1-p2)=-0.04.

p_d=p_1-p_2=0.07-0.11=-0.04

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{44+255}{627+2314}=\dfrac{299}{2941}=0.102$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.102*0.898}{627}+\dfrac{0.102*0.898}{2314}}\\\\\\s_{p1-p2}=\sqrt{0.000146+0.000039}=\sqrt{0.000185}=0.014$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.014}=\dfrac{-0.04}{0.014}=-2.9398$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$\text{P-value}=2\cdot P(z$

As the P-value (0.0033) is smaller than the significance level (0.05), the effect is significant. This P-value shows the probability of having this outcome (sample results) given that the null hypothesis is true.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in the use of eReaders by different age groups.

If we have used the critical value approach, the critical value for a two-tailed test is zc=±1.96. If the test statistic falls within the range of the critical values, the null hypothesis is failed to be rejected.

In this case, the test statistic is smaller than zc=-1.96, so it falls in the rejection region and the null hypothesis is rejected.

Researchers conducted a study to find out if there is a difference in the use of eReaders by differe

answered: Guest

you need to show the graph

step-by-step explanation:

answered: Guest

the answer is 0.3175 hope that you ^w^

also you might actually want to put this picture up if you want people to solve it luckily i remember this question

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Researchers conducted a study to find out if there is a difference in the use of eReaders by differe...