QNT 351 Week 5 Problems

1. Which hypothesis, the null or the alternative, is the status-quo hypothesis?

2. What is the level of significance of a test of hypothesis?

3. For each of the following rejection regions, sketch the sampling distribution for z and indicate the location of the rejection region, and determine the probability that a Type I error will be made.

4. A survey found that 55% of college professors believe that their online education courses are as good as or superior to courses that use traditional face-to-face instruction.

5. A university economist conducted a study of elementary school lunch menus. During the state-mandated testing period, school lunches averaged 881 calories. The economist claimed that after the testing period ended, the average caloric content of the school lunches increased significantly. Set up the null and alternative hypothesis to test the economist’s claim.

6. A random sample of 100 observations from a population with standard deviation 65 yielded a sample mean of 111. Complete parts a trough c.

a. Test the null hypothesis that µ=100 against the alternative hypothesis that µ>100, using α=0.05. Interpret the results of the test.

b. Test the null hypothesis that µ=100 against the alternative hypothesis that µ≠100, using α=0.05. Interpret the results of the test.

c. Compare the results of the two tests you conducted. Explain why the results differ. Choose the correct answer bellow.

7. A study of n=59 hospital employees found that the number of latex gloves used per week by the sampled workers is summarized by x = 23.1 and s = 13.7. Let µ represent the mean number of latex gloves used per week by all hospitals employees. Consider testing H0: µ=27 against Ha: µ<27.

a. Give the rejection region for the test at a significance level of α=0.01

b. Calculate the value of the test statistic

c. Use the results, parts a and b, to make the appropriate conclusion

8. A satellite photograph of an urban area was divided into 4x4 meter areas (called pixels). Of interest is a numerical measurement of the distribution of gaps or hole sizes in the pixel, called lacunarity. The mean and standard deviation of the lucanarity measurements of 800 pixels randomly selected from a specific urban area are 223 and 19, respectively. It is known that the mean lacunarity measurements for all grassland pixels is 219. Do the data suggest that the area sampled is grassland? Test at α=0.01

What is the rejection region for the test? Choose the correct answer bellow.

What is the value of the test statistic?

What is the appropriate conclusion at a=0.01?

9. In order to compare the means of two populations, independent random sample of 390 observations are selected from each population, with the results found in the table to the right. Complete parts a trough e.

a. Use a 95% confidence interval. Select the correct answer from the options bellow.

b. Test the null hypothesis H0:(µ1 - µ2) = 0 versus the alternative hypothesis Ha: (µ1-µ2)≠0. Give the significance level of the test, and interpret the result.

c. Suppose the test in part b was conducted with the alternative hypothesis Ha:(µ1-µ2) > 0. How would you answer to part b change?

d. Test the null hypothesis H0: (µ1-µ2) = 22 versus Ha: (µ1-µ2)≠22. Give the significance level, and interpret the results.

e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a-d?

10. To use the t-statistic to test for a difference between the means of two populations, what assumptions must be made about the two populations? About the two samples?

What assumption must be made about the two populations? Select all that apply.

What assumption must be made about the two samples? Select all that apply.

11. The data in the table to the right resulted from an experiment that utilized a completely randomized design. Use this information to complete parts a and b

12. A survey was conducted to determine the impact of contamination on property values. Home owners were randomly selected from each of seven states – A, B, C, D, E, F and G. Each homeowner was asked to estimate the property value of a home located in an area contaminated by a certain substance. The dependent variable of interest was the substance discount percentage ( the difference between the current home value and the estimated value after contamination , as a percentage ). The researchers were interested in comparing the mean substance discount percentages across the seven states. Complete parts a and b.

a. Give the null and alternative hypotheses of interest to the researchers. Choose the correct answer bellow.

b. An ANOVA summary table is shown to the right. Use the information provided to conduct the hypothesis test, part a. Use a = 0.10

What is the rejection region? Select the correct choice bellow and fill in the answer boxes to complete your choice.

Determine the conclusion for the hypothesis test. Choose the correct answer bellow.

13. In the production of commercial eggs in a region, four different types of housing systems for the chickens are used: cage, barn, free range, and organic. The characteristics of eggs produced from the four systems were investigated. Twenty-five commercial grade A eggs were randomly selected from supermarket-10 of which were produced in cages, 5 in barns with free range, and 5 organic. A number of quantitative characteristics compared the means of the four housing systems, Minitab descriptive statics and AVONA pointouts for each characteristic are shown in the accompanying display. Fully interpret the results. Identify the characteristic for which housing systems differ.

14. Explain what each of the following sample correlation coefficients tells you about the relationship between the x and y values in the sample.

a. r=1     b. r=-1    c. r=0    d. r=0.9    e. r=0.08    f. r= -0.97

a. What relationship exists between the x and y values in the sample?

b. What relationship exists between the x and y values in the sample?

c. What relationship exists between the x and y values in the sample?

d. What relationship exists between the x and y values in the sample?

e. What relationship exists between the x and y values in the sample?

f. What relationship exists between the x and y values in the sample?

15. A study was conducted to determine if taller people earn more money over their career than short people. Using data collected from 2244 individuals from various careers, the researchers computed the correlation between average earnings over the past decade and height. The result are given in the table. Complete parts a through e below