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 groups. In the $16$- to $29$-year-old group, $7\%$of the $628$surveyed use eReaders, while of the $2,309$participants $30$years old and older use eReaders.

Short answer

(a) The null hypothesis is that $p1=p2$.

(b) Alternate hypothesis is, $p1\ne p2$.

(c) The random variable is the difference in the percentage of electronic readers by age group.
(d) Normal distribution.
(e) Using the two-sample t-test option of Minitab and filling in all the requirements,

Test statistics- $3.30$.

(f) P- value $0.0003$.

(g) Graph regions to the $p$-value.

i) $\alpha =0.05$.

ii) Decision: Null hypothesis is rejected.

iii) Reason for decision: p-value is >$\alpha$.

iv) From the sample data, there is enough evidence to conclude that the proportion of eReader users 16 to 29 years old differs from the proportion of eReader users 30 and older at the 5% significant level.

Step-by-step solution

Given information

Determine if there is a variation in the use of e-readers by various age groups.

Explanation

(a) The null hypothesis is defined as follows:

$p_1=p_2$.

(b) The null hypothesis is defined as follows:

$p\ne P$

(c) The random variable is the difference between the proportions of e-readers by different age groups.

(d) Normal distribution

(e) By using the sample test option, fill in all the requirements.

Step 3: 

After you've entered all of the values, you'll get the result displayed below.

Test & CI for two proportions

Sample	X	N	Sample p
1	44	628	0.070064
2	254	2309	0.110004

Difference = $p\left(1\right)-p\left(2\right)$
Estimated difference:$-0.0399406$
Test for difference =$0$(vs not =$0$) : Z=$-3.30$P-Value =$0.001$
Fishers exact test p value is$0.0003$

Test statistics -$3.30$

Step 4: 

(f) The output has a p-value of$0.003$.

(g) Draw a graph of the regions that correspond to the p-value.

(h)

Step 5:

i) $\alpha =0.01$

ii) The null hypothesis must be rejected.

iii) Reason for Decision is $p$−value is greater than $\alpha$.

iv) From the sample data, there is enough evidence to conclude that the proportion of eReader users $16$to $29$years old differs from the proportion of eReader users $30$and older at the $5\%$significant level.