Question

Faculty members at a large university are irritated by students’ cell phones. The faculty has found over the past several semesters that a cell phone rings in class on average 20 times per semester. A reporter for the school newspaper claims that students are more courteous with their cell phones now than in past semesters, and that the average has decreased. The reporter finds that in a random sample of 19 classes, the average number of times a cell phone rang last semester was 18.3 with a standard deviation of 2.7 calls. Does the evidence support the reporters claim? Assume that the number of cell phone rings is normally distributed.
State the appropriate null and alternative hypotheses.

Conduct a test of the hypotheses identified above. Use Statcrunch or another computer software option to find the following. Please copy/paste the results into this document.

I. Calculate the test statistic
II. Calculate the corresponding p-value.(again, use statcrunch)
III. Make a statistical decision using level of significance of 0.05. Justify your decision.
IV. Interpret your decision in the context of the problem.

At the top of your document, please include your Name, Section number, Id number.

Answer 1

Answer:

The claim is having statistical evidence.

Step-by-step explanation:

Given that faculty members at a large university are irritated by students’ cell phones. The faculty has found over the past several semesters that a cell phone rings in class on average 20 times per semester.

$H_0: \bar x = 20\\H_a: \bar x$

(left tailed test at 5% confidence)

$\bar x = 18.3\\s=2.7\\n = 19\\se = \frac{2.7}{\sqrt{19} } \\=0.6194$

Mean difference = -1.7

Test statitstic t = mean diff/std error = -2.744

df =18

p value = 0.006671

Since p < 0.05 we reject H0

The claim is having statistical evidence.