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# Variety of Statistics Problems

I have attached a series of statistical problems. Please provide as much detail as possible. I want to double check my answers for each question.

1. A chain of health-food stores is determining the relationship between the number of times its commercial is broadcast on radio or television weekly and the weekly sales volume. It randomly selects nine weeks and determines the number of times the commercial was broadcast and the corresponding weekly volume of sales as shown below:

Number of Times Weekly Sales Volume
Commercial is Broadcast (in thousands of dollars)
x y

3 42
4 47
5 52
7 72
8 85
9 100
10 115
12 185
20 225

a. Determine the least-squares prediction equation for the line of best fit.
b. Calculate the standard error of the estimate.
c. What is the predicted sales volume when the commercial is broadcast 15 times weekly on the radio or television?

2. The U.S. Food and Drug Administration (FDA) bans the use of hormones in poultry production. Nevertheless, a recent University of California study found the 10% of the consumers surveyed said that they ate less poultry because of concern over hormones. To check on this claim, 84 consumers are randomly selected and it is found that ten of them eat less poultry because of their concern over hormones. Should we reject the results of the University of California study? (Use a 5% level of significance and be sure to include the critical values and test statistic in your answer)

a. Give the null and alternative hypothesis.
b. Give the test statistic and critical values.
c. Would you reject the null or fail to reject the null hypothesis?

3. A 1993 editorial in the Journal of the American Medical Association cited a review of 43 recently published studies. In 26 of them, researchers had found that low calcium intake by humans was linked to bone mass, bone loss, or fractures. Find a 95% confidence interval for the true proportion of studies linking low calcium intake by humans to bone mass, bone loss, or fractures.

4. A publisher wishes to determine the list price for a new algebra book. A survey of the list price of eight competing books sold by other companies showed an average price of \$39.95 with a standard deviation of \$2.85. Construct a 95% confidence interval for the average list price of a new algebra book.

5. An obstetrician wants to learn whether the amount of prenatal care and the wantedness of the pregnancy are associated. He randomly selects 939 women who had recently given birth and asks them to disclose whether their pregnancy was intended, unintended or mistimed. In addition, they were to disclose when they started receiving prenatal care, if ever. The results of the survey are as follows:

Wantedness of Months Pregnant Before Prenatal Care Began
Pregnancy Less than 3 mos. 3 to 5 mos. More than 5 mos.

Intended 593 26 33
Unintended 64 8 11
Mistimed 169 19 16

a. Using a 5% level of significance, test the null hypothesis for whether the frequency of the wantedness of the pregnancy is independent when the prenatal care began.
b. Compute the chi-square test statistic.

6. The following data represents the flight time (in minutes) of a random sample of seven flights from Los Angeles, Nevada to Newark, New Jersey, on Continental Airlines.

282, 270, 260, 266, 257, 260, 267
a. Compute the range, mode, mean, and median.
b. Compute the variance and standard deviation.

7. The following data represent the hemoglobin (in g/dL) for 20 randomly selected cats:
5.7 8.9 9.6 10.6 11.7
7.7 9.4 9.9 10.7 12.9
7.8 9.5 10.0 11.0 13.0
8.7 9.6 10.3 11.2 13.4

a. Compute the z-score corresponding to the hemoglobin of Buttercup, 7.8 g/dL.
b. Determine the quartiles.
c. Compute the interquartile range, IQR.

8. A large trucking company that delivers fresh fruit wishes that its truck drivers be forced to work overtime. The union claims that the more hours that a truck driver works, the greater the risk of an accident (due to fatigue). To support its claim, the union has gathered the following statistics on the average number of hours worked by a truck driver (per week) and the average number of accidents (per week).

# of Hours Worked: 35 37 39 42 44 46 50
------------------------------------------------------------------------------------------------------------
# of Accidents 1.6 2.2 3.8 4.3 5.6 6.1 7.3

a. Determine the least-squares prediction equation.
b. Calculate the standard error of the estimate.
c. What is the predicted number of accidents when a truck driver is forced to work 48 hours a week.

9. The manager of the Night-All Corporation recently conducted a survey of 196 of its employees to determine the average number of hours that each employee sleeps at night. The company statistician submitted the following information to the management:
∑x = 1479.8 and ∑(x - x bar)2 = 1755
Where x is the number of hours slept by each employee. Find a 95% confidence interval estimate for the average number of hours each employee sleeps at night (be sure to include the critical values in your answer).

10. The following data represent the annual number of days over 1000F for Dallas - Ft. Worth from 1`905 to 2004.

Number of Number of
Days Years
0 - 9 31
10 - 19 39
20 - 29 17
30 - 39 6
40 - 49 4
50 - 59 2
60 - 69 1

a. Find the mean number of days at over 1000
b. Find the standard deviation.

#### Solution Preview

Hi there,

Thanks for selecting me as your expert. I've included my explanation in the word document.

1. A chain of health-food stores is determining the relationship between the number of times its commercial is broadcast on radio or television weekly and the weekly sales volume. It randomly selects nine weeks and determines the number of times the commercial was broadcast and the corresponding weekly volume of sales as shown below:

Number of Times Weekly Sales Volume
Commercial is Broadcast (in thousands of dollars)
x y

3 42
4 47
5 52
7 72
8 85
9 100
10 115
12 185
20 225

a. Determine the least-squares prediction equation for the line of best fit.
b. Calculate the standard error of the estimate.
c. What is the predicted sales volume when the commercial is broadcast 15 times weekly on the radio or television?

a) Mean of x: (3+4+5+7+8+9+10+12+20)/9=8.666667
SSx=(3-8.666667)^2+(4-8.666667)^2+...+(20-8.666667)^2=212
Mean of y: (42+47+52+...+225)/9=102.5556
Sxy=(3-8.666667)*(42-102.5556)+(4-8.666667)*(47-102.5556)+...+(20-8.666667)*(225-102.5556)= 2528.667
Slope=Sxy/Sxx=2528.667/212=11.92767
Bo=mean of y-slope*mean of x=102.5556-11.92767*8.666667=-0.81754
Therefore, the equation for the regression line is y=11.92767x-0.81754.

b)To find out the standard error, we first need to find out the residuals for every x.
For example, when x=3, predicted y=11.92767*3-0.81754=34.96547
Residual=42-34.96547=7.03453
With the similar approach, we could figure out all the residuals and come up with the following table:
x y predicted y residual
3 42 34.96547 7.03453
4 47 46.89314 0.10686
5 52 58.82081 -6.82081
7 72 82.67615 -10.6762
8 85 94.60382 -9.60382
9 100 106.53149 -6.53149
10 115 118.45916 -3.45916
12 185 142.3145 42.6855
20 225 237.73586 -12.7359

Standard error=sqrt((7.03453^2+0.10686^2+...+12.7359^2)/(9-2))= 18.28783

c) When x=15, y=11.92767*15-0.81754=178.0975
Therefore, the predicted sales volume is around 178 thousands of dollars.

2. The U.S. Food and Drug Administration (FDA) bans the use of hormones in poultry production. Nevertheless, a recent University of California study found the 10% of the consumers surveyed said that they ate less poultry because of concern over hormones. To check on this claim, 84 consumers are randomly selected and it is found that ten of them eat less poultry because of their concern over hormones. Should we reject the results of the University of California study? (Use a 5% level of significance and be sure to include the critical values and test statistic in your answer)

a. Give the null and alternative hypothesis.
b. Give the test statistic and critical values.
c. Would you reject the null or fail to reject the null hypothesis?

a) Null hypothesis: p=0.10 (p is the proportion of consumers who ate less poultry because of concern over ...

#### Solution Summary

The variety of statistics problems are examined.

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