Question

**Sleep – College Students:** Suppose you perform a
study about the hours of sleep that college students get. You know
that for all people, the average is about 7 hours. You randomly
select 50 college students and survey them on their sleep habits.
From this sample, the mean number of hours of sleep is found to be
6.2 hours with a standard deviation of 0.97 hours. We want to
construct a 95% confidence interval for the mean nightly hours of
sleep for all college students.

(a) What is the point estimate for the mean nightly hours of
sleep for all college students?

hours

(b) What is the critical value of *t* (denoted
*t*_{α/2}) for a 95% confidence interval?
**Use the value from the table or, if using software, round
to 3 decimal places.**

*t*_{α/2} =

(c) What is the margin of error (*E*) for a 95% confidence
interval? **Round your answer to 2 decimal
places.**

*E* = hours

(d) Construct the 95% confidence interval for the mean nightly
hours of sleep for all college students. **Round your answers
to 1 decimal place.**

< *μ* <

(e) Based on your answer to (d), are you 95% confident that the
mean nightly hours of sleep for all college students is below the
average for all people of 7 hours per night? Why or why not?

Yes, because 7 is above the upper limit of the confidence interval for college students.

No, because 7 is below the upper limit of the confidence interval for college students.

Yes, because 7 is below the upper limit of the confidence interval for college students.

No, because 7 is above the upper limit of the confidence interval for college students.

(f) We are never told whether or not the parent population is
normally distributed. Why could we use the above method to find the
confidence interval?

Because the sample size is less than 100.

Because the margin of error is positive.

Because the margin of error is less than 30.

Because the sample size is greater than 30.

Answer #1

This can be solved using excel<data<megastat<confiedence intervals:

Here is the output:

Confidence interval - mean | ||

95% | confidence level | |

6.2 | mean | |

0.97 | std. dev. | |

50 | n | |

2.010 | t (df = 49) | |

0.276 | margin of error | |

5.924 | lower confidence limit | |

6.476 | upper confidence limit |

a) The point estimate for the mean nightly hours of sleep for all college students is the sample mean = 6.2

b) critical value =2.010

c) E= 0.28

d) 5.9 < *μ* <6.5

e) YES, because 7 is above the upper limit of the confidence interval for college students.

f) Because the sample size is greater than 30.

Please do the comment for any doubt or clarification. Please upvote if this helps you out. Thank You!

Sleep – College Students: Suppose you perform a study about
the hours of sleep that college students get. You know that for all
people, the average is about 7 hours. You randomly select 45
college students and survey them on their sleep habits. From this
sample, the mean number of hours of sleep is found to be 6.2 hours
with a standard deviation of 0.97 hours. We want to construct a 95%
confidence interval for the mean nightly hours of...

Sleep
– College Students: Suppose you perform a study about the hours of
sleep that college students get. You know that for all people, the
average is about 7 hours. You randomly select 45 college students
and survey them on their sleep habits. From this sample, the mean
number of hours of sleep is found to be 6.2 hours with a standard
deviation of 0.97 hours. We want to construct a 95% confidence
interval for the mean nightly hours of...

Sleep – College Students: Suppose you perform a
study about the hours of sleep that college students get. You know
that for all people, the average is about 7 hours. You randomly
select 40 college students and survey them on their sleep habits.
From this sample, the mean number of hours of sleep is found to be
6.2 hours with a standard deviation of 0.86 hours. We want to
construct a 99% confidence interval for the mean nightly hours of...

Suppose you perform a study about the hours of sleep that
college students get. You know that for all people, the average is
about 7 hours. You randomly select 35 college students and survey
them on their sleep habits. From this sample, the mean number of
hours of sleep is found to be 6.2 hours with a standard deviation
of 0.97 hours. We want to construct a 95% confidence interval for
the mean nightly hours of sleep for all college...

Suppose you perform a study about the hours of sleep that
college students get. You know that for all people, the average is
about 7 hours. You randomly select 35 college students and survey
them on their sleep habits. From this sample, the mean number of
hours of sleep is found to be 6.2 hours with a standard deviation
of 0.97 hours. We want to construct a 99% confidence interval for
the mean nightly hours of sleep for all college...

Suppose you perform a study about the hours of sleep that
college students get. You know that for all people, the average is
about 7 hours. You randomly select 35 college students and survey
them on their sleep habits. From this sample, the mean number of
hours of sleep is found to be 6.4 hours with a standard deviation
of 0.97 hours. You want to construct a 95% confidence interval for
the mean nightly hours of sleep for all college...

Sleep – College Students: Suppose you perform a
study about the hours of sleep that college students get. You know
that for all people, the average is about 7 hours. You randomly
select 40 college students and survey them on their sleep habits.
From this sample, the mean number of hours of sleep is found to be
6.1 hours with a standard deviation of 0.97 hours. You want to
construct a 99% confidence interval for the mean nightly hours of...

Sleep – College Students: Suppose you perform a study about
the hours of sleep that college students get. You know that for all
people, the average is about 7 hours. You randomly select 45
college students and survey them on their sleep habits. From this
sample, the mean number of hours of sleep is found to be 6.1 hours
with a standard deviation of 0.86 hours. You want to construct a
99% confidence interval for the mean nightly hours of...

Sleep – College Students: Suppose you perform a
study about the hours of sleep that college students get. You know
that for all people, the average is about 7 hours. You randomly
select 45 college students and survey them on their sleep habits.
From this sample, the mean number of hours of sleep is found to be
6.1 hours with a standard deviation of 0.97 hours. You want to
construct a 99% confidence interval for the mean nightly hours of...

Suppose you perform a study about the hours of sleep that
college students get. You know that for all people, the average is
about 7 hours. You randomly select 35 college students and survey
them on their sleep habits. From this sample, the mean number of
hours of sleep is found to be 6.2 hours with a standard deviation
of 0.97 hours. You want to construct a 99% confidence interval for
the mean nightly hours of sleep for all college...

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