Question

1. The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 44 for a sample of size 22 and standard deviation 6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level).
Give your answers to one decimal place and provide the point estimate with its margin of error. __________________ ± ________________________

2. In a survey, 31 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $10. Estimate how much a typical parent would spend on their child's birthday gift (use a 95% confidence level).
Give your answers to one decimal place. Provide the point estimate and margin or error. _______________ ± _________________

3. You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:

13.8
65.2
51.2
22.5
41.7
13.8
58.4
39.4
32.2
31.1

Find the 80% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 80% C.I. = ___________________
Answer should be obtained without any preliminary rounding.

4. The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 38.9 for a sample of size 339 and standard deviation 13.4. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level).
Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
_________< μ < __________

5. Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 7 with a mean of 52.6 and a standard deviation of 14.3 at a confidence level of 99.9%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. = ________________    Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

6. Express the confidence interval (337.6,540.6)(337.6,540.6) in the form of ¯x ± ME.

¯x ± ME= ___________ + ______________

7. Assume that a sample is used to estimate a population mean μμ. Find the 95% confidence interval for a sample of size 66 with a mean of 27.9 and a standard deviation of 20.8. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

95% C.I. = _____________
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

8. Assume that a sample is used to estimate a population proportion μμ. Find the margin of error M.E. that corresponds to a sample of size 411 with a mean of 20.9 and a standard deviation of 20.6 at a confidence level of 90%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =__________________
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

9. In a survey, 16 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $38 and standard deviation of $7. Estimate how much a typical parent would spend on their child's birthday gift (use a 95% confidence level).
Give your answers to one decimal place. Provide the point estimate and margin or error. _____________ ± _______________

10. Assume that a sample is used to estimate a population mean μμ. Find the 90% confidence interval for a sample of size 56 with a mean of 59.2 and a standard deviation of 13.2. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
90% C.I. = _________________
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

11. Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 21 with a mean of 58.7 and a standard deviation of 17.9 at a confidence level of 80%.
Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. = _______________
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

12. Express the confidence interval (174.8,273.6) in the form of ¯x ± ME.

¯x ± ME=_________________

13. Assume that a sample is used to estimate a population proportion μμ. Find the margin of error M.E. that corresponds to a sample of size 45 with a mean of 15.3 and a standard deviation of 6.6 at a confidence level of 99%.
Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. = ________________
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

14. You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:

32.1
30.7
9
22.2
42.7
-5.8
20.5
20.8
52.4
28.6
9.2

Find the 90% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place).
90% C.I. = _________________

15. The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 30.9 for a sample of size 889 and standard deviation 11.3. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level).
Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
___________< μ < ____________________

16. You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:

74.2
89.8
70.1
81.7
63.6
94.8
75.3
73.3
76
66.3
63

Find the 80% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 80% C.I. = _____________________

17. The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 50 for a sample of size 19 and standard deviation 8. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level).
Give your answers to one decimal place and provide the point estimate with its margin of error.
______________ ± _______________

Answer 1

1)

sample std dev ,    s =    6.0000
Sample Size ,   n =    22
Sample Mean,    x̅ =   44.0000

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   21          
't value='   tα/2=   2.0796   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   6.0000   / √   22   =   1.279204
margin of error , E=t*SE =   2.0796   *   1.27920   =   2.7

confidence interval = x̅ ± E = 44 ± 2.7

2)

sample std dev ,    s =    10.0000
Sample Size ,   n =    31
Sample Mean,    x̅ =   42.0000
Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   30          
't value='   tα/2=   2.0423   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   10.0000   / √   31   =   1.796053
margin of error , E=t*SE =   2.0423   *   1.79605   = 3.7

confidence interval = x̅ ± E = 42 ± 3.7

3)Level of Significance ,    α =    0.20
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   17.7239
Sample Size ,   n =    10
Sample Mean,    x̅ = ΣX/n =    36.9300

degree of freedom=   DF=n-1=   9          
't value='   tα/2=   1.3830   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   17.7239   / √   10   =   5.604781
margin of error , E=t*SE =   1.3830   *   5.60478   =   7.751573
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    36.93   -   7.751573   =   29.178427
Interval Upper Limit = x̅ + E =    36.93   -   7.751573   =   44.681573
80%   confidence interval is (   29.18   < µ <   44.68   )