Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. the organization thinks that, currently, the mean is higher. fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. the sample mean was 4.75 hours with a sample standard deviation of 2.0. conduct a hypothesis test. the null and alternative hypotheses are:

The teenagers spent 4.5 hours per week, on average, on the phone.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 4.5

Sample mean, = 4.75

Sample size, n = 15

Alpha, α = 0.05

Sample standard deviation, s = 2

First, we design the null and the alternate hypothesis

We use one-tailed(right) t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,                  

We accept the null hypothesis.  Thus, the teenagers spent 4.5 hours per week, on average, on the phone. The sample contradicted the organization's claim.

There is no evidence that the population mean is greater than hours.

Step-by-step explanation:

Given:

Step 1 :

Null hypothesis:

Alternative hypothesis:  

Since the alternative hypothesis has a greater than symbol, it is a right-tailed hypothesis test.

Significance level is

Step 2:

The Test statistic of the organization

The p-value for a right-tailed test is given by:  

Step 3:

Now,

at level of significance, degree of freedom

Since,

so, accept the null hypothesis. Thus, the teenagers spent hours per week, on average, on the phone. The sample contradicted the organization's claim.

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