Question

Two computer users were discussing tablet computers. A higher proportion of people ages $16$to $29$use tablets than the proportion of people age $30$and older. Table localid="1653641949025" $10.28$details the number of tablet owners for each age group. Test at the localid="1653641953436" $1\%$level of significance.

Table.localid="1653641957518" $10.28$

	localid="1653641961619" $16-29$years old	localid="1653641966431" $30$years old and older
Own table	69	231
Sample size	628	2309

Short answer

At the $1\%$level of significance, there is insufficient evidence from the sample data to establish that a greater proportion of tablet owners are between the ages of $16$and $29$than those between the ages of $30$and older.

Step-by-step solution

Given information

Given in the question that,

$\begin{array}{|lll|}\hline & \mathbf{16}\mathbf{-}\mathbf{29}\text{year olds}& \mathbf{30}\text{years old and older}\\ \text{Own a Tablet}& 69& 231\\ \text{Sample Size}& 628& 2,309\\ \hline\end{array}$

Explanation

(a) The null hypothesis is defined as follows: $p_1\le p_2$.

(b) The alternate hypothesis is defined as follows: $p_1>p_2$

(c) Between the proportions of age groups, the random variable is varied.

(d) Two proportions have a normal distribution.

(e) Fill in all requirements using Minitab's two-sample $t$-test option.

The result will be:

Part 3: Conclusion

The test statistics : $0.70$.

From the output, the $p$value is: $0.458$.

Using the data from the last exercise, create a mental picture of the situation.

The horizontal axis should be clearly labelled and scaled, and the region(s) matching to the $p-value$should be shaded on the graph.

$\alpha =0.01$

Accept the null hypothesis as a conclusion.

$p-value>\alpha$is the reason for the decision.