# Statistics Problems

2. For each of the following, indicate whether the factor influences the numerator or denominator of the z score and determine whether the effect would be to increase the value of z (further from zero) or decrease the value of z (closer to zero). In each case, assume that all other components of the z score remain constant.

a. increase the sample size

b. increase the population standard deviation

c. increase the difference between the sample mean and the value of mean specified in the null hypothesis.

8. A researcher would like to test the effectiveness of a newly developed growth hormone. The researcher knows that under normal circumstances laboratory rats each an average weight of mean =950 grams at 10 weeks of age. The distribution of weights in normal with sd =30. A random sample of n=25 newborn rates is obtained, and the hormone is given to each rat. When the rats in the sample each 10 wks old, each rat is weighted. The mean weight for this sample is M=974.

a. identify the independent and the dependent variables.

b. assuming a two tailed test, state the null hypothesis in a sentence that includes the independent and the dependent variables.

c. using symbols, state the hypothesis (H0 and H1) for this two tailed test.

d. sketch the appropriate distribution, and locate the critical region for alpha =.05

e. calculate the test statistics (z score) of the sample

f. what decision should be made about the null hypothesis, and what decision should be make about the effect of the hormone?

18. A sample of n=9 scores is obtained from a normal population distribution with sd=12. The sample mean =60.

a. with a two tailed test and alpha =.05, use the sample data to test the hypothesis that the population mean is 65.

b. with a two tailed test and alpha test and alpha =.05. use the sample data to test the hypothesis that the population mean is 55.

c. in parts (a) and (b) of this problem, you should find that mean =65 and mean =55 are both acceptable hypotheses. Explain how two different values can both be acceptable.

20. A sample of n =16 individuals is selected from a population that forms a normal distribution with mean=40. A treatment is administered to the sample and, after treatment, the sample is measured to evaluate the effect of the treatment.

a. assuming that the population sd is 8, compute Cohen's d to measure the effect size for a sample mean =42.

b. assuming sd=2, compute Cohen's d to measure the effect size for a sample mean of M =42.

c. assuming sd =8, compute Cohen's d to measure the effect size for a sample mean of M=48.

d. assuming sd =2, compute Cohen's d, to measure the effect size for a sample mean of

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#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.

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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