Testing the hypothesis, we have that:
a)
The null hypothesis is: 
The alternative hypothesis is: 
b) The p-value of the test is of 0.1212.
c) Since the <u>p-value of the test is of 0.1212 > 0.05</u>, we cannot conclude that the mean daily number of texts for 25–34 year olds differs from the population daily mean number of texts for 18–24 year olds.
d) Since <u>|z| = 1.55 < 1.96</u>, we cannot conclude that the mean daily number of texts for 25–34 year olds differs from the population daily mean number of texts for 18–24 year olds.
Item a:
At the null hypothesis, we <u>test if the mean is the same</u>, that is, of 128 texts every day, hence:

At the alternative hypothesis, we <u>test if the mean is different</u>, that is, different of 128 texts every day, hence:

Item b:
We have the <u>standard deviation for the population</u>, thus, the z-distribution is used. The test statistic is given by:
 
The parameters are:
 is the sample mean.
 is the sample mean.
 is the value tested at the null hypothesis.
 is the value tested at the null hypothesis.
 is the standard deviation of the population.
 is the standard deviation of the population.
n is the sample size.
For this problem, the values of the parameters are: 
Hence, the value of the test statistic is:



Since we have a two-tailed test, as we are testing if the mean is different of a value, the p-value is P(|z| < 1.55), which is 2 multiplied by the p-value of z = -1.55.
Looking at the z-table, z = -1.55 has a p-value of 0.0606
2(0.0606) = 0.1212
The p-value of the test is of 0.1212.
Item c:
Since the <u>p-value of the test is of 0.1212 > 0.05</u>, we cannot conclude that the mean daily number of texts for 25–34 year olds differs from the population daily mean number of texts for 18–24 year olds.
Item d:
Using a z-distribution calculator, the critical value for a <u>two-tailed test</u> with <u>95% confidence level</u> is |z| = 1.96.
Since <u>|z| = 1.55 < 1.96</u>, we cannot conclude that the mean daily number of texts for 25–34 year olds differs from the population daily mean number of texts for 18–24 year olds.
A similar problem is given at brainly.com/question/25369247