Stastics exam

MATH 105 - Worksheet Week 9 Names:

1. The p-value for a hypothesis test is .06. For each of the following signifi-

cant levels, decide whether the null hypothesis should be rejected.

(a) α=.05 Fail to reject H0

(b) α=.10 Reject H0

2. Which provides stronger evidence against the null hypothesis, a p-value

of .06 or a p-value of .01?

A p-value of .01 gives stronger evidence.

3. The US Substance Abuse and Mental Health Services Administration

conducts surveys on drug use by type of drug and age group. Results

are published in National Household Survey on Drug Abuse. According

to that publication, 15.0% of the 18-25 year-olds were current users of

marijuana in 2000. We are interested in whether recent evidence supports

that there has been a change in marijuana use since 2000.

(a) State the null and alternative hypotheses for test the claim that the

proportion of marijuana users has changed since 2000. H0 : p = .15

versus H1 : p ̸= .15 where p is the proportion of 18-25 year-olds that use marijuana.

(b) A recent poll of 1283 randomly selected 18-25 year-olds revealed that

205 currently use marijuana or hashish. Calculate p̂.

p̂ = 2051283 = .160

(c) Report the p-value.

z = .16− .15√

.15∗.85 1283

= 0.98

p-value=2*(1-.8365)=0.327

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(d) Did you find sufficient evidence of a change since 2000 in drug use

among this age group? Give a one sentence conclusion.

No, the p-value was greater than .05 so we did not find sufficient evi-

dence to conclude that the proportion of marijuana users is different

than 15%.

(e) A confidence interval for the proportion of marijuana users in 2014

is (0.140< p <0.180)which is interpreted: We can be 95% confident

that between 14% and 18% of 18-25 year-olds use marijuana. Is the

confidence interval consistent with your conclusion in d)? Explain.

The results of the hypothesis test are in agreement with the confi-

dence interval since we did not find that p is different than 0.15 (the

confidence interval includes 0.15).

4. A researcher is interested in whether college students get enough sleep.

She suspects that they get less than 8 hours of sleep on average. The

sample mean (x̄) for 65 students was 7.08 hours. The standard deviation

of number of hours students slept is s=1.8.

(a) Determine the null and alternative hypothesis for the test. What is

the parameter in this study?

H0 : µ = 8

H1 : µ < 8

µ is the mean number of hours of sleep college students get.

(b) The p-value for the test is <0.0001. Using a significance level of .05,

write a one or two sentence conclusion in context of the problem.

Since the p-value is less than 0.05, we can reject H0 and conclude that

on average college students get less than 8 hours of sleep per night.

(c) A 95% confidence interval for µ for the above data is (6.634< µ <7.53).

Interpret the confidence interval. Be sure to use the word mean or

average in your interpretation and don’t forget units.

We can be 95% confident that college students get between 6.634 and

7.53 hours of sleep on average each night.

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(d) Does your confidence interval support the results of the hypothesis

test? Explain.

Yes, the conclusion for the hypothesis test was that students get less

than 8 hours of sleep per night and the confidence interval is consistent

with this since it does not include 8.

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