Question

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 groupsin the to 29year-old group7% of the 628 surveyed use ereaders, while 11of the 2,309 participants 30 years old and older use ereaders(use subscripts let 1 16- to 29-year-old users , and 230 years old and

Answer 1

No, there is significant difference in the use of e readers by different age groups.

Given sample 1 ( 29 years old) $n_{1}$=628, $p_{1}$=7%, sample 2( 30 years old)$n_{2}$=2309, $p_{2}$=0.11.

We have to first form hypothesis one null hypothesis and other alternate hypothesis.

$H_{0}:$π1-π2=0

$H_{1}:$π1-π2≠0

α=0.05

Difference between proportions $p_{1}-p_{2} =-0.04$

$p_{d}=0.07-0.11=-0.04$

The pooled proportion needed to calculate standard error is:

$p=(X_{1} -X_{2} )/(n_{1} +n_{2} )$

=(44+254)/(628+2309)

=0.10146

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

$S_{p_{1} -p_{2} }=\sqrt{p(1-p)/m_{1}+p(1-p)/n_{2} }$

=$\sqrt{0.101*0.899/628+0.101*0.899/2309}$

=$\sqrt{0.000143+0.00003}$

=$\sqrt{0.000173}$

=0.01315

Z= Pd-(π1-π2)/$S_{p_{1} -p_{2} }$

=-0.04-0/0.013

=-3.0769

This test is a two tailed test so the p value for this test is calculated as (using z table)

p value:2 P(Z<-3.0769)

=2*0.002092

=0.004189

P value< significance level of 5%.

Hence there is enough evidence to show the claim that there is a significant difference in the use of e readers by different age groups.

Learn more about hypothesis at brainly.com/question/11555274

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Question is incomplete as it also includes:

Significance level of 5%.