Question

In: Statistics and Probability

A researcher at the Annenberg School of Communication is interested in studying the use of smartphones...

A researcher at the Annenberg School of Communication is interested in studying the use of smartphones among young adults. She wants to know the average amount of time that college students in the United States hold a smartphone in their hand each day. The researcher obtains data for one day from a random sample of 25 college students (who own smartphones). She installs an app that registers whenever the smartphone is being held and the screen is on. The sample mean is 230 minutes, with a standard deviation of 11 minutes.

What is the 99% confidence interval for average daily time a smartphone is used among college students?

What is the lower bound of the confidence interval?   

What is the upper bound of the confidence interval?

What decision should the researcher make about the null hypothesis? Be sure to explain your answer (e.g., what numbers provide the basis for this decision?).

Would our decision about the null hypothesis have been different if the researcher had initially hypothesized that women spend more time talking on their phones than men?

Explain all parts/information necessary to answer this question.

Solutions

Expert Solution

n = 25

s = 11

confidence level = c = 0.99

Here population standard deviation is not known, so we will use here t distribution.

99% confidence interval for average daily time a smartphone is used among college students is

Where tc is t critical for degrees of freedom = n - 1 = 25 - 1 = 24 and confidence level = c = 0.99

tc = 2.797                   (Round to 3 decimal)

99% confidence interval for average daily time a smartphone is used among college students is (223.8466, 236.1534)

lower bound of the confidence interval = 223.8466

upper bound of the confidence interval = 236.1534

Average amount of time that college students in the United States hold a smartphone in their hand each day will lie between 223.8466 and 236.1534.

Yes our decision about the null hypothesis have been different if the researcher had initially hypothesized that women spend more time talking on their phones than men.

orchestra answered 1 year ago
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