Question

Q1. What is the sampling distribution? Would the sampling distribution of the median be normally distributed for the following distribution? Why or why not? 70 60 50 Frequency 40 30 20 10 0 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 Q2. What happens to the standard error of the sampling distribution as we increase sample size? Why? Q3. What is the relationship between standard error and certain that the mean we observed in our sample is close to the population mean? Why? Q4. A team of researchers is investigating the sleep patterns of adults in a city. The average nightly sleep duration for the entire adult population is µ = 7 hours, with a standard deviation of a = 1 hour. The researchers randomly select a sample of 150 adults for their study. What is the probability that the average nightly sleep duration for the researcher's sample of 150 adults will be between 6 and 7.5 hours? Remember to use standard error in your z-score calculation (mean/(sd/sqrt(n)))

          Q1. What is the sampling distribution? Would the sampling distribution of the median be
normally distributed for the following distribution? Why or why not?
70
60
50
Frequency
40
30
20
10
0
11-20
21-30
31-40
41-50
51-60
61-70
71-80
81-90
91-100
Q2. What happens to the standard error of the sampling distribution as we increase
sample size? Why?
Q3. What is the relationship between standard error and certain that the mean we
observed in our sample is close to the population mean? Why?
Q4. A team of researchers is investigating the sleep patterns of adults in a city. The
average nightly sleep duration for the entire adult population is µ = 7 hours, with a
standard deviation of a = 1 hour. The researchers randomly select a sample of 150
adults for their study.
What is the probability that the average nightly sleep duration for the researcher's
sample of 150 adults will be between 6 and 7.5 hours? Remember to use standard error
in your z-score calculation (mean/(sd/sqrt(n)))

Show more…

Q1. What is the sampling distribution? Would the sampling distribution of the median be
normally distributed for the following distribution? Why or why not?
70
60
50
Frequency
40
30
20
10
0
11-20
21-30
31-40
41-50
51-60
61-70
71-80
81-90
91-100
Q2. What happens to the standard error of the sampling distribution as we increase
sample size? Why?
Q3. What is the relationship between standard error and certain that the mean we
observed in our sample is close to the population mean? Why?
Q4. A team of researchers is investigating the sleep patterns of adults in a city. The
average nightly sleep duration for the entire adult population is µ = 7 hours, with a
standard deviation of a = 1 hour. The researchers randomly select a sample of 150
adults for their study.
What is the probability that the average nightly sleep duration for the researcher's
sample of 150 adults will be between 6 and 7.5 hours? Remember to use standard error
in your z-score calculation (mean/(sd/sqrt(n)))

Added by Laura G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ahmet Yavas

02/23/2023

Step 1

It represents the distribution of a sample statistic, such as the mean or median, across all possible samples of a certain size from a population. Show more…

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Q1.What is the sampling distribution? Would the sampling distribution of the median be normally distributed for the following distribution? Why or why not? 70 60 20 10 2021.30.11.101.50.51.6101180 Q2.What happens to the standard error of the sampling distribution as we increase sample size? Why? Q3.What is the relationship between standard error and certain that the mean we observed in our sample is close to the population mean? Why? average nightly sleep duration for the entire adult population is =7 hours,with a standard deviation of g =1 hour.The researchers randomly select a sample of 150 adults for their study What is the probability that the average nightly sleep duration for the researcher's sample of 150 adults will be between 6 and 7.5 hours? Remember to use standard error in your z-score calculation(mean/(sd/sqrt(n))

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Transcript

00:01 In this question, there is given a standard normal distribution, and for this distribution, we know that the mean, which is denoted by mu, should be zero, and the standard deviation, denoted by sigma, should be one here.

00:13 So we can define the random variable z, which is normally distributed.

00:16 This is zero and one here.

00:18 So what we have to do for, let's say this is the first question, so this is the probability of z.

00:24 So between the mean and z is equal to 0 .45.

00:27 So the mean is 0, and this is less than z.

00:30 Less than .45.

00:32 In order to get this probability, i'm going to use the graphing display calculator application, the normal cdf, lower boundary is 0 .545, the mean and the standard division, which is press second variance and the normal cdf, lower boundary is zero, the upper boundary is 0 .45, the mean and the standard division, so the probability would be 0 .17 and 36.

00:55 And the next one, which is between the mean and z is equal to negative 80.

01:03 So this is negative 1 .80, z and 0.

01:07 So again, i'm going to use the normal cdf function, the lower boundary negative 1 .80, the upper boundary is 0.

01:14 The mean and the standard division, which is press second variance, the normal cdf, negative 1 .80, and the upper boundary is 0, and the mean is 0, and the standard division is 1, which is.

01:26 So let me take.

01:27 The probability would be which is 0 .46 and 41 here.

01:32 In the next step where the z value is less than negative 1 .5 this is negative 0 .95 to get this probability again i'm going to use the normal cdf function there is no lower boundary put very small number the upper boundary negative 0 .95 the mean and the standard division which is press second variance the normal cdf negative 1 second 899 upper boundary is negative 0 .95, the mean and the standard division.

02:01 So the answer would be which is 0 .17 and 11 here.

02:07 And also there is one more question here.

02:10 So for the second question there is given the mean value here and we have the normal distribution...

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