Question

According to a social media blog, time spent on a certain social networking website has a mean of 24 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 7 minutes.

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 23.5 and 24.5 minutes? (Round to three decimal places as needed.)

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 23 and 24 minutes? (Round to three decimal places as needed.)

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 23.5 and 24.5 minutes? (Round to three decimal places as needed.)

d. Explain the difference in the results of (a) and (c).

The sample size in (c) is greater than the sample size in (a), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is____________________ (less/greater) than in (a). As the standard error ____________________ (increases/decreases) values become more concentrated around the mean. Therefore, the probability that the sample mean will fall in a region that includes the population mean will always ____________________ (decrease/increase) when the sample size increases.

Answer #1

Here it is given that distribution is normal and also population standard deviation is known, so sample mean is also normally distributed

a. Here we need to find

b.

c.

d. The sample size in (c) is greater than the sample size in (a), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is less than in (a). As the standard error decreases values become more concentrated around the mean. Therefore, the probability that the sample mean will fall in a region that includes the population mean will always increase when the sample size increases.

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social networking website has a mean of 23 minutes per visit.
Assume that time spent on the social networking site per visit is
normally distributed and that the standard deviation is 4 minutes.
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sample of 36 ?sessions, what is the probability that the sample
mean is between 22.5 and 23.5 ?minutes? nothing ?(Round to three
decimal places...

According to a social media blog, time spent on a certain
social networking website has a mean of 17 minutes per visit.
Assume that time spent on the social networking site per visit is
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a. If you select a random sample of 16
sessions, what is the probability that the sample mean is
between
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(Round to three decimal places as...

According to a social media blog, time spent on a certain
social networking website has a mean of 20 minutes per visit.
Assume that time spent on the social networking site per visit is
normally distributed and that the standard deviation is 6 minutes.
Complete parts (a) through (d) below.
a. If you select a random sample of 16 sessions, what is the
probability that the sample mean is between 19.5 and 20.5 minutes?
(Round to three decimal places as...

According to a social media blog, time spent on a certain
social networking website has a mean of 17 minutes per visit.
Assume that time spent on the social networking site per visit is
normally distributed and that the standard deviation is 7 minutes.
Complete parts (a) through (d) below.
a. If you select a random sample of
36sessions, what is the probability that the sample mean is
between 16.5 and 17.5 minutes?
b. If you select a random sample...

According to a social media blog, time spent on a certain
social networking website has a mean of 16 minutes per visit.
Assume that time spent on the social networking site per visit is
normally distributed and that the standard deviation is 5
minutes.
If you select a random sample of 36 sessions, what is the
probability that the sample mean is between 15.5 and 16.5
minutes?
(Round your answer to three decimal places)

According to a social media blog, time spent on a certain
social networking website has a mean of 18 minutes per visit.
Assume that time spent on the social networking site per visit is
normally distributed and that the standard deviation is 4
minutes.
If you select a random sample of 100 sessions, what is the
probability that the sample mean is between 17.5 and 18.5
minutes?

Suppose a geyser has a mean time between eruptions of 79
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distributed with standard deviation 22 minutes. Complete parts (a)
through (e) below.
(a) What is the probability that a randomly selected time
interval between eruptions is longer than 90 minutes? The
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90 minutes is approximately nothing. (Round to four decimal places
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(b) What is the probability...

A researcher records the amount of time (in minutes) that
parent-child pairs spent on social networking sites to test whether
they show any generational differences. From the following findings
reported in APA format, interpret these results.
Parents spent significantly less time on social networking sites
compared to their children
(MD = 42 minutes),
t(29) = 3.343,
p < 0.05,
d = 0.61.
State the research design used (repeated measures or matched
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repeated measures designmatched pairs
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State the sample...

A researcher records the amount of time (in minutes) that
parent-child pairs spent on social networking sites to test whether
they show any generational differences. From the following findings
reported in APA format, interpret these results.
Parents spent significantly less time on social networking sites
compared to their children
(MD = 42 minutes),
t(29) = 3.225,
p < 0.05,
d = 0.75.
State the research design used (repeated measures or matched
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-repeated measures design
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State...

A study showed that in a certain month, the mean time spent per
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Write down your P-value.
Round your answer to...

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