A. Calculate the point estimate of mu (sample mean, xbar) for 2.282, 4.96, 6, 8.

Question

A.    Calculate the point estimate of mu (sample mean, xbar) for 2.282, 4.96, 6, 8.54 and enter your response to two decimals (i.e. 1.12). Use Excel's AVERAGE function.

B.    Calculate the difference (absolute value) the sample mean (point estimate, statistic, xbar) 25.3 is from a population where the mean (parameter, mu) is 32.6. Enter your response to one decimal (i.e. 32.1).

C.    Calculate the sample standard deviation for 2.05, 16.8, 69.49. Enter your response to two decimals (i.e. 1.23). Use Excel's STDEV function.

D.    Calculate the estimate of the standard deviation (standard error) of the mean (sigma xbar) where the sample standard deviation is 19.7761 and the sample size is 18. Enter your answer to two decimals (i.e. 1.12).

E.    Calculate the degrees of freedom that would be used in determining the value of t to be used in developing a confidence interval of the mean if the sample size was 21. Enter your response as an integer (i.e. 39).

F.     Determine the confidence level where the value of t is 1.2393 that would be used in calculating the confidence interval estimate of the mean using a sample size 11. Enter your response to two decimals (i.e. 0.95). Use the TDIST function. Check to see that your value appears appropriate using the t table in your book.

G.    Determine the value of t (critical value) that would be used in calculating the 85% confidence interval estimate of the population mean (mu) for a sample size 26 and enter your response to four decimals as shown in the t distribution table (i.e. 1.1234). Use the TINV function. Check to see that your value appears appropriate using the t table in your book.

H.    Calculate the margin of error (e) if the sample size was 15, the sample standard deviation (s) was 18.73 and a confidence level of 95% (t=2.1448) is used. Enter your response to two decimal places (i.e. 39.12).

I.      Calculate the upper limit of the confidence interval of the mean if the sample size (n) was 18, the sample standard deviation (s) was 6.7737, a confidence level of 95% (t=2.1098) was needed, and the sample mean (xbar) was 29.4362. Enter your response to one decimal place (i.e. 21.1).

J.      Assuming Utahns sleep an average of 6 hours and the confidence interval, created from sample data for another population, is 5.5 to 5.9, what can we conclude about the population from which the sample was selected?   

1.     there is sufficient evidence to conclude that Utahns sleep at least a tenth of an hour more than the population from which the sample was selected

2.     there is insufficient evidence to conclude that Utahns sleep a different amount than the population from which the sample was selected

3.     none of these

4.     there is sufficient evidence to conclude that Utahns sleep at least a tenth of an hour less than the population from which the sample was selected

K.    Calculate the sample size required for a confidence interval estimate of a population mean where the desired margin of error (e) is 4, the assumed population standard deviation (sigma) is 15.54, and the confidence level is 95% (critical z=1.96). Enter your response as an integer and remember to round as indicated in the text for sample size.

L.    Calculate the point estimate of the population proportion (sample proportion) if the sample size (n) is 3,675 and the number in the sample exhibiting the attribute/characteristic you are interested in (x) is 288. Enter your response to three decimal places (i.e. 0.123).

M.   Calculate the estimate of the standard deviation (standard error) of the sampling distribution of proportions to be used in calculating the confidence interval limits if your sample of (n=2,555) had (x=212) that exhibited the attribute/characteristic you are interested in. Enter your response to four decimal places (i.e. 0.1234).

N.    Determine the confidence level where the value of z is 1.18 that would be used in calculating the confidence interval estimate of the population proportion and enter your response to two decimals (i.e. 0.12). Use the NORMSDIST function. Check to see that your value appears appropriate using the standard normal distribution (z) table in your book.

O.    Determine the positive value of z that would be used in developing an interval estimate of a population proportion where the confidence level to be used is 93%. Use the NORMSINV function and enter your response to two decimal places (i.e. 1.12).

P.     Calculate the margin of error for the sampling distribution of proportions if the sample size is 1,715 and the number exibiting the attribute of interest is 110. Assume a confidence level of 95% is used. Enter your response rounded to three decimal places (i.e. 0.123). Use NORMSINV to determine the value of z that you need for this calculation.

Q.    Calculate the upper limit of the confidence interval to estimate the population proportion if the sample size (n) was 1,477, a confidence level of 95% is desired (use z=1.96), and 169 (x) exhibited the attribute/characteristic you are interested in. Enter your response to three decimal places (i.e. 0.123).

R.    Calculate the largest sample size that would be required for an interval estimate of a population proportion where the desired margin of error (e) is 0.02, use 0.50 as the population proportion in the formula, and the confidence level is 90% (use z=1.645). Enter your response as an integer and round as indicated in the text for determining the sample size.

S.     Calculate the sample size required for an interval estimate of a population proportion where the desired margin of error (e) is 0.07, the best guess for the population proportion is 0.3 obtained from a pilot sample, and the confidence level is 90% (use z=1.645). Enter your response as an integer and round as indicated in the text for determining the sample size.

T.    Assuming the percentage of Utah home mortgages behind one-or-more payments is 5% and the confidence interval, created from sample data for another state, is 3.8 to 4.3, what can we conclude about the state from which the sample was selected?

1.     there is sufficient evidence to conclude that the percentage of home mortgates behind one-or-more payments in that state is higher than in Utah

2.     there is sufficient evidence to conclude that the percentage of home mortgates behind one-or-more payments in that state is lower than in Utah

3.     there is insufficient evidence to conclude that the percentage of home mortgates behind one-or-more payments in that state is different from Utah

4.     none of these

Explanation / Answer

a.
Mean = Sum of observations/ Count of observations
Mean = (2.282 + 4.96 + 6 + 8.54 / 4) = 5.4455
b.
mean diffrence b/w them is = 32.6 - 25.3 = 32.6 - 25.3
c.
Mean = Sum of observations/ Count of observations
Mean = (2.05 + 16.8 + 69.49 / 3) = 29.4467
Variance
Step 1: Add them up
2.05 + 16.8 + 69.49 = 88.34
Step 2: Square your answer
88.34*88.34 =7803.9556
…and divide by the number of items. We have 3 items , 7803.9556/3 = 2601.3185
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
2.05^2 + 16.8^2 + 69.49^2 = 5115.3026
Step 4: Subtract the amount in Step 2 from the amount in Step 3
5115.3026 - 2601.3185 = 2513.9841
Step 5: Subtract 1 from the number of items in your data set, 3 - 1 = 2
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
2513.9841 / 2 = 1256.992
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
35.4541

e.
critical value
the value of |t | with n-1 = 20 d.f

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