Question

The following data represent the number of days absent per year in a population of six employees of a small company. 1, 3, 6, 7, 9, 10 Required (a) Assuming that you simple without replacement, select all possible samples of n=2 and construct the sampling distribution of the mean. Compute the mean of all the sample means and also compute the population mean.​

Answer 1

Step-by-step explanation:

The following data represent the number of days absent per year in a population of six employees of a small company. Complete parts (a) through (d). 1, 3, 4, 6, 9, 10 Print (a) Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distribution of the mean. Compute the mean of all the sample means and also compute the population mean. Are they equal? What is this property called? Construct the sampling distribution of the mean. Choose the correct graph below. Frequency Karba Frequency Frequency 12 Meanin=2) Maan (n=2 6 Mean (n=2) Meen (n=2) The mean of all the sample means for n=2 without replacement is (Round to two decimal places as needed.) The population mean is (Round to two decimal places as needed.) Are the mean of all the sample means and the population mean equal? What is this property called? Choose the correct answer below. O A. The mean of all the sample means for n=2 without replacement and the population mean are equal. This property is called the unbiased property of the sample mean. OB. The mean of all the sample means for n = 2 without replacement and the population mean are equal. This property is called the unbiased property of the population mean. Oc. The mean of all the sample means for n = 2 without replacement and the population mean are not equal. This property is called the unbiased property of the population mean. OD. The mean of all the sample means for n=2 without replacement and the population mean are not equal. This property is called the unbiased property of the sample mean. (b) Repeat part (a) for all possible values of n=3. Construct the sampling distribution of the mean. Choose the correct answer below. OA WO Acanbod Roonbow Frequency 6 Meanin-3) 11 Mean (3) 612 Mean (1-3) Means) The mean of all the sample means for n = 3 without replacement is (Round to two decimal places as needed.) The mean of all the sample means for n = 3 without replacement and the population mean are (1). (c) Compare the shape of the sampling distribution of the mean in parts (a) and (b). Which sampling distribution has less variability? Why? Choose the correct answer below. O A. The distribution for n=2 without replacement has less variability because the sample means cluster closer to the population mean, H. OB. The distribution for n= 3 without replacement has less variability because the sample means cluster closer to the population mean, I. OC. The distribution for n = 2 without replacement has less variability because there are fewer possible values the sample mean could take. (d) Assuming that you sample with replacement, repeat (a) through (c) and compare the results. Which sampling distributions have the least variability—those in the new part (a) or the new part (b)? Why? Construct the sampling distribution for n=2 with replacement. Choose the correct graph below. Frequency Frequency Freuency Frequency 11 6 Mean (n=2) 12 Mean (n=2) Moan (n=2) Mean (n=2) Construct the sampling distribution for n = 3 with replacement. Choose the correct graph below. Kuantan Frequency Frequency Frequency 11 Mecan (n=3) Mesan (n=3) 6 Mesari in=3) Mean (n=3) Which sampling distributions have the least variability—those in the new part (a) or the new (b)? Why? O A. The distribution for n = 3 with replacement has less variability because the sample means cluster closer to the population mean, H. O B. The distribution for n = 2 with replacement has less variability because the sample means cluster closer to the population mean, H. OC. The distribution for n=2 with replacement has less variability because there are fewer possible values the sample mean could take. (1) O O not equal. equal.

Answer 2

Concept Introduction:-

It could take the shape of a word or a numerical representation of a quantity's arithmetic value.

Given Information:-

We have been given that the following data represent the number of days absent per year in a population of six employees of a small company. $1, 3, 6, 7, 9, 10$

To Find:-

We have to find that assuming that you simple without replacement, select all possible samples of $n=2$ and construct the sampling distribution of the mean. Compute the mean of all the sample means and also compute the population mean.​

Solution:-

According to the problem

$Mean=\frac{1+3+6+7+9+10}{6}\\ =\frac{36}{6}\\=6$

The table is the probability table for the sample mean and it is the sampling distribution of the sample mean weights of the populations when the sample size is $2$. It is also worth noting that the sum of all the probabilities equals $1$. It might be helpful to graph these values.

Final Answer:-

The attachment shows the population graph and the sample mean is $6$.

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