Question

(1 point)
Weights of 10 red and 36 brown randomly chosen M{\&}M plain candies are listed below.

Red: 0.9080.9090.9070.920.9360.8980.8980.8740.9130.9240.9080.9070.9360.8980.9130.9090.920.8980.8740.924
Brown: 0.9090.9150.9550.9140.9310.9090.9050.930.8570.8770.9660.9020.920.9040.8660.8710.8720.9280.9880.920.8580.8980.9360.9210.9850.8750.9290.90.9230.8610.8670.8760.9020.8970.9180.9130.9090.9050.920.9880.9850.8670.9150.930.9040.920.8750.8760.9550.8570.8660.8580.9290.9020.9140.8770.8710.8980.90.8970.9310.9660.8720.9360.9230.9180.9090.9020.9280.9210.8610.913
1.    To construct a 95% confidence interval for the mean weight of red M{\&}M plain candies, you have to use
A. The t distribution with 11 degrees of freedom
B. The normal distribution
C. The t distribution with 9 degrees of freedom
D. The t distribution with 10 degrees of freedom
E. None of the above
2.    A 95% confidence interval for the mean weight of red M{\&}M plain candies is
<μ<<μ<  
3.    To construct a 95% confidence interval for the mean weight of brown M{\&}M plain candies, you have to use
A. The normal distribution
B. The t distribution with 36 degrees of freedom
C. The t distribution with 35 degrees of freedom
D. The t distribution with 37 degrees of freedom
E. None of the above
4.    A 95% confidence interval for the mean weight of brown M{\&}M plain candies is
<μ<<μ<

(1 point)

Among the most exciting aspects of a university professor's life are the departmental meetings where such critical issues as the color the walls will be painted and who gets a new desk are decided. A sample of 20 professors was asked how many hours per year are devoted to such meetings. The responses are listed below. Assuming that the variable is normally distributed with a standard deviation of 6 hours, estimate the mean number of hours spent at departmental meetings by all professors. Use a confidence level of 94%.

6,10,13,7,13,5,4,7,15,15,6,4,22,9,15,16,17,5,18,146,13,13,4,15,6,22,15,17,18,10,7,5,7,15,4,9,16,5,14

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

(1 point)

The data below are the ages of a random sample of 8 men in a bar. It is known that the population of ages are normally distributed with a standard deviation of 9. Determine the 97% confidence interval estimate of the population mean.

53,66,25,37,56,43,28,4853,66,25,37,56,43,28,48

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

(1 point) The following random sample was selected from a normal distribution:

164811910410106164811910410106

(a)    Construct a 9090% confidence interval for the population mean μμ.
≤μ≤≤μ≤

(b)    Construct a 9595% confidence interval for the population mean μμ.
≤μ≤≤μ≤

(1 point)

The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 13. A random sample of 330 salespeople was taken and the mean number of cars sold annually was found to be 73. Find the 92% confidence interval estimate of the population mean.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

(1 point)

How many rounds of golf do those physicians who play golf play per year? A survey of 12 physicians revealed the following numbers:

7,39,16,3,34,42,22,16,18,31,10,487,39,16,3,34,42,22,16,18,31,10,48

Estimate with 94% confidence the mean number of rounds played per year by physicians, assuming that the population is normally distributed with a standard deviation of 7.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

(1 point) Periodically, the county Water Department tests the drinking water of homeowners for contminants such as lead and copper. The lead and copper levels in water specimens collected in 1998 for a sample of 10 residents of a subdevelopement of the county are shown below.

lead (μμg/L)	copper (mg/L)
1.11.1	0.3780.378
0.10.1	0.7520.752
4.64.6	0.8210.821
5.65.6	0.2170.217
1.11.1	0.7530.753
5.75.7	0.0040.004
3.23.2	0.7260.726
1.51.5	0.3540.354
2.32.3	0.7320.732
2.62.6	0.3180.318

(a)    Construct a 9999% confidence interval for the mean lead level in water specimans of the subdevelopment.
≤μ≤≤μ≤

(b)    Construct a 9999% confidence interval for the mean copper level in water specimans of the subdevelopment.  
≤μ≤≤μ≤

(1 point) The scientific productivity of major world cities was the subject of a recent study. The study determined the number of scientific papers published between 1994 and 1997 by researchers from each of the 20 world cities, and is shown below.

City	Number of papers	City	Number of papers
City 1	2323	City 11	1717
City 2	1616	City 12	33
City 3	55	City 13	2424
City 4	3030	City 14	2626
City 5	1818	City 15	2525
City 6	2626	City 16	2020
City 7	2525	City 17	44
City 8	1616	City 18	1919
City 9	1010	City 19	2424
City 10	2525	City 20	3030

Construct a 9797 % confidence interval for the average number of papers published in major world cities.

<μ<<μ<

Answer 1

1:

Following is out put of descriptive statistics:

Descriptive statistics
	Red	Brown
count	10	36
mean	0.90870	0.90828
sample standard deviation	0.01687	0.03308
sample variance	0.00028	0.00109
minimum	0.874	0.857
maximum	0.936	0.988
range	0.062	0.131

1:

Here we have

Here population standard deviation is unknown so t-distrbution will be used. The degree of freedom:

df =n-1=9

Correct option:

C. The t distribution with 9 degrees of freedom

2:

Critical value of t for 95% confidence interval, using excel function "=TINV(0.05,9)", is 2.262.

The required confidence interval is

3:

Here we have

Here population standard deviation is unknown so t-distrbution will be used. The degree of freedom:

df =n-1=35

Correct option:

C. The t distribution with 35 degrees of freedom

4:

Critical value of t for 95% confidence interval, using excel function "=TINV(0.05,35)", is 2.030.

The required confidence interval is