# Statistics Problems

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial:n = 6, x = 2, p = 0.45.

0.278

0.208

0.003

0.057

Use the Poisson distribution to find the indicated probabilities. Currently, 11 babies are born in the village of Westport (population of 760) each year. Find the mean number of births per day.

0.0301

0.9700

0.0297

0.9699

Comparing Scores. Three students take equivalent tests of a sense of humor and, after the laughter dies down, their scores are calculated. Which score is in the middle of the other two?

1. A score of 144 on a test with a mean of 128 and a standard deviation of 34?

2. A score of 90 on a test with a mean of 86 and a standard deviation of 18?

3. A score of 18 on a test with a mean of 15 and a standard deviation of 5?

Answer 1.

Answer 2.

Answer 3.

Cannot determine from the information provided

Comparing Scores. Three students take equivalent tests of a sense of humor and, after the laughter dies down, their scores are calculated. Which is the lowest relative score?

1. A score of 144 on a test with a mean of 128 and a standard deviation of 34?

2. A score of 90 on a test with a mean of 86 and a standard deviation of 18?

3. A score of 18 on a test with a mean of 15 and a standard deviation of 5?

Answer 1.

Answer 2.

Answer 3.

Cannot determine from the information provided.

The values in the table are measured maximum breadths of male Egyptian skulls from different time periods. Changes in head shape over time suggest that interbreeding occurred with immigrant populations. Use a 0.05 level of significance to test the claim that the different time periods do not all have the same mean.

4000 B.C. 1850 B.C. 150 A.D.

131 129 128

138 134 138

125 136 136

129 137 139

132 137 141

135 129 142

132 136 137

134 138 145

138 134 137

The critical value of the statistic is?

4.0497

3.4028

27

Can not compute the critical value of the statistic from the given data.

A student lives in a home with a solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and the results are listed in the accompanying table. Use a 0.05 significance level to test the claim that the mean voltage reading is the same for the three different types of day.

Sunny Days Cloudy Days Rainy Days

13.5 12.7 12.1

13.0 12.5 12.2

13.2 12.6 12.3

13.9 12.7 11.9

13.8 13.0 11.6

14.0 13.0 12.2

The critical value of the statistic is?

38.0379

3.6823

18

81.4

In the 107th Congress, the Senate consists of 13 women and 87 men. If a lobbyist for the tobacco industry randomly selects three different senators, what is the probability that they are all women?

0.17700

0.01770

0.00177

0.82300

You have just started your own Airline. You have one plane for a route connecting Austin, Boise, and Chicago. One route is Austin-Boise-Chicago and a second route is Chicago-Boise-Austin. How many other routes are possible?

1.

2.

3.

4.

Determine whether the given value is a statistic or a parameter: A sample of students is

selected and the average (mean number of textbooks purchased this semester is 4.2).

Statistic.

Parameter

Identify which type of sampling is used:Exit Poll. CNN is planning an exit poll in which 100 polling stations will be randomly selected and all voters will be interviewed as they leave the premises.

Random.

Systematic.

Convenience.

Stratified.

Cluster.

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#### Solution Summary

This posting provides solution to several types of statistics problems including elementary statistics, hypothesis testing, ANOVA, Sampling etc.

Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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