Sleep Time A person read that the average number of hours an adult sleeps on Friday night to Saturday morning was 6.9 hours. The researcher f that college students do not sleep 6.9 hours on average. The researcher randomly selected 14 students and found that on average they slept 7.5 hc The standard deviation of the sample is 1.4 hours. At a=0.05, is there enough evidence to say that college students do not sleep 6.9 hours on average? Assume that the population is approximately normally distributed. Use critical value method and tables. Part: 0 / 5 Part 1 of 5 (a) State the hypotheses and identify the claim. H: (Choose one) ▼ H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.
Sleep Time A person read that the average number of hours an adult sleeps on Friday night to Saturday morning was 6.9 hours. The researcher f that college students do not sleep 6.9 hours on average. The researcher randomly selected 14 students and found that on average they slept 7.5 hc The standard deviation of the sample is 1.4 hours. At a=0.05, is there enough evidence to say that college students do not sleep 6.9 hours on average? Assume that the population is approximately normally distributed. Use critical value method and tables. Part: 0 / 5 Part 1 of 5 (a) State the hypotheses and identify the claim. H: (Choose one) ▼ H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Sleep Time A person read that the average number of hours an adult
sleeps on Friday night to Saturday morning was 6.9 hours. The researcher feel
that college students do not sleep 6.9 hours on average. The researcher
randomly selected 14 students and found that on average they slept 7.5 hours.
The standard deviation of the sample is 1.4 hours. At a=0.05, is there enough
evidence to say that college students do not sleep 6.9 hours on average?
Assume that the population is approximately normally distributed. Use the
critical value method and tables.
Part: 0 / 5
Part 1 of 5
(a) State the hypotheses and identify the clainm.
H:
(Choose one) ▼
H :
(Choose one) ▼
This hypothesis test is a (Choose one) ▼ test.
Transcribed Image Text:Sample Question
Sleep Time A person read that the average number of
hours an adult sleeps on Friday night to Saturday morning
was 7.4 hours. The researcher feels that college students sleep
less than 7.4 hours on average. The researcher randomly
selected 16 students and found that on average they slept
6.2 hours. The standard deviation of the sample is 1.1 hours. At
a= 0.05, is there enough evidence to say that college students
sleep less than 7.4 hours on average? Assume that the
population is approximately normally distributed. Use the
critical value method and tables.
(a) State the hypotheses and identify the claim.
(b) Find the critical value.
(c) Compute the test value.
(d) Make the decision.
(e) Summarize the results.
Explanation
(a) State the hypotheses and identify the claim.
The null hypothesis H, is the statement that there is no
difference between a parameter and a specific value. This is
equivalent to H: u=7.4 hours.
The alternative hypothesis H, is the statement that there is
a difference between a parameter and a specific value. In this
case, college students sleep less than 7.4 hours on average.
This is equivalent to H,: µ<7.4 hours.
The problem asks, "Do college students sleep less than 7.4
hours on average?"
Hence, the claim is the alternative hypothesis.
(b) Find the critical value.
From eThe t Distribution Table, for a one-tailed test with a-0.05 and
d.f. - 16-1-15, the critical value is --1.753.
The t Distribution Table
Confidence
intervals
80%
90%
95%
98%
99%
One tail, a
0.10
0.05
0.025
0.01
0.005
Two tails,
d.f.
0.20
0.10
0.05
0.02 0.01
14
1.345
1.761
2.145
2.624
2.977
15
1.341
1.753
2.131
2.602
2.947
16
1.337
1.746
2.120
2.583 2.921
(c) Compute the test value.
The i test is a statistical test for the mean of a
population and is used when the population is
normally or approximately normally distributed and
o is unknown.
The formula for the test is
The degrees of freedom are d.f. =n- 1.
Using the formula for the r-test,
6.2 -7.4
1.1//16
--4.364
Hence, the test value, rounded to 3 decimal places, is
I--4.364.
(d) Make the decision.
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