Revision Exercises on ttests and nonparametricsolution.docx

1、Revision Exercises on ttests and nonparametricsolutionREVISION EXERCISES ON T-TESTS AND NON-PARAMETRIC TESTSQuestion 1File: CountryThe following results is to test the null hypothesis that the average life expectancy for males is the same as the average life expectancy for females (variables: lifeex

2、pm and lifeexpf). Interpret the results.Ho: diff = 0Ha: diff = 0diff: mean difference between male and female life expectancySig. = 0.000. Results are significant at the 0.1% level. Female life expectancy is significantly higher (mean = 66.31) than male life expectancy (mean = 61.9)Question 2File: g

3、ssInterpret the results above.AgeHo: 1 = 2Ha: 1 2Where 1 and 2 are mean age for people who belief and dont belief in life after deathSig. = 0.338. Results are not significant. There is no significant difference in mean age for people who belief and dont belief in life after death.EducationHo: 1 = 2H

4、a: 1 2Where 1 and 2 are mean years of education for people who belief and dont belief in life after deathSig. = 0.551. Results are not significant. There is no significant difference in mean years of education for people who belief and dont belief in life after death.Question 3File: SalaryThe follow

5、ing is a non-parametric test to test the relationship between years on the job between males and females for clerical workers. Interpret the results.Ho: There is no difference in the job seniority of males and femalesHa: There is significant difference in the job seniority of males and femalesSig. =

6、 0.725. Results are not significant. There is no significant difference in the job seniority of males and femalesQuestion 4File: gssThe following data is restricted to husbands and wives, both of whom are emplyed full time (wrkstat = 1; spwrksta=1). A non-parametric test was performed to see if husb

7、ands and wives work the same number of hours a week (husbhr and wifehr). Interpret your results. Interpret the resultsHo: There is no difference in the hours worked of husbands and wivesHa: There is a significant difference in the hours worked of husbands and wivesSig. = 0.000. Results are significa

8、nt at the 0.1% level. Husbands work longer hours than wives. Question 5Below are two box plots on home prices in the Northeast Region (NE = Yes) and other regions (NE = Non) in Albuquerque. The dotted lines represent the mean values.a) What can you say about the variation in the two groups? What sta

9、tistical measure is used to measure this variation and what aspect of the box plot depicts this measure? Name two other measures of variation. b) Comment on the distribution of price for the two groups. What is the implication of this in terms of the choice of statistical tests? c) Would the mean or

10、 median be a better measure to compare the price of houses between the two groups? Why? d) What is your comment on the prices of houses in the two areas? e) Give one advantage of using the box plot over the histogram. f) State a test that would be suitable to analyse the difference in home prices be

11、tween the two regions. a) The variation in the two groups are different. The North east sector has a higher variation than the other sectors. (1m) The statistical measure used to measure the variation is the interquartile range and it is represented by the length of the box plot. (2m). Other measure

12、s of variation are such as the standard deviation and the coefficient of variation. (1m)b) For the Northeast sector, the price is slightly positively skewed, for other regions, the price is slightly negatively skewed. This implies that the types of test chosen should be non-parametric tests. (3m)c)

13、The median would be a better measure because the distribution is skewed. (2m)(d) The box plot shows that the price of houses is approximately equal but the variation in price is higher for North east regions compared to other regions. (2m)(e)The box plot shows the measures of central tendency and va

14、riation whereas the bar chart only shows the measures of central tendency and not variation. (1m).f) Mann WhitneyQuestion 6The following output is obtained from a data set containing a random sample of nursing homes collected by the Department of Health and Social Services in New Mexico. Youve been

15、asked to examine the data and determine whether there is a difference in revenue generated by rural and non-rural nursing homes. You generated the following output.a) Did you use pooled (equal var) or unspooled (unequal) variance for the t-test? Explain. b) Interpret the test to determine whether th

16、ere is a difference in revenue generated by rural and non-rural nursing homes. Include in your interpretation, the null and alternative hypothesis. a) Ho: Equal variance assumedHa: Equal variance not assumedSig. = 0.445 5% Do not reject Ho. Equal variance assumed Use pooled variance (2m)b) Ho: 1 = 2

17、Ha: 1 2 (1m)Where: 1 and 2 are the mean revenue of rural and non rural areas respectively.(1m)Results are significant at the 5% level.(1m) This shows that there is a significant difference in the mean revenue between rural and non-rural nursing homes. The revenue for non-rural homes is higher than r

18、ural homes.(2m).Question 7Determine whether the following tests are paired or independent.a) An economist wishes to determine whether there is a difference in mean family income for households in 2 socioeconomic groups. b) Youre a marketing research analyst. You want to compare a clients calculator

19、to a competitors. You sample 8 retail stores. a) independentb) paired Question 8For the following studies, indicate whether an independent-samples or paired t-test is appropriate:(i) You want to study the gender differences in the spending habits of young adults. You select 400 males and 300 females

20、 to study their spending behaviour.(2 marks)(ii) Consumer preferences for Pizza Huts new “Hawaiian X-tra Persona” pizza were obtained on 7-point Likert scale. The same consumers were then shown a commercial about this new pizza. After the commercial, consumers preference for the new pizza, were meas

21、ured. Has the commercial been successful in inducing a change in preference?(2 marks)i) Independentii) pairedQuestion 9A trainer has developed a new method for improving the sales of salespersons. To evaluate the new method, he compared the sales of each of 10 salespersons before and after the train

22、ing. The following SPSS output was produced: Paired Samples TestPaired differencestdfSig. (2-tailed)MeanStd. DeviationStd. Error MeanPair after training- 1 before training4.303.4011.0753.9989.003Interpret the results(4 marks)H0 mdiff= 0H1 mdiff 0Where mdiff is the mean difference in sales before and

23、 after training. Sig. = 0.003. Results are significant at the 1% level. Mean sales has significantly increased by an average of 4.3 after training. Question 10 A researcher wants to study the gender differences in the current salaries of employees in a marketing division of Mars & Venus Ltd at the 5

24、% significance level. He obtained the following outputs when using SPSS:Group StatisticsCurrent SalaryGenderNMeanStd. DeviationStd. ErrorMeanFemale216$26031.9$7,558.021$514.258Male258$41441.8$19,499.214$1,213.968Independent Samples TestLevenes Test for Equality of Variancest-test for Equality of Mea

25、nsFSig.tdfSig.(2-tailed) MeanDifferenceCurrent SalaryEqual variances assumed119.67.000-10.95472.000- $15,409.86Equal variances not assumed-11.69344.26.000-$15,409.86Interpret the resultsHo: 1=2Ha: 12Where 1and 2 are mean salary for males and femalesSig. = 0.000. Results are significant at the 0.1 %

26、level. The mean salary of males is significantly higher (mean = 41441) than females (mean = 26031). Question 11Indicate which non-parametric test (Mann-Whitney U Test, Wilcoxon matched-pairs signed-ranks test, and Kruskal-Wallis Test) you would use in each of the following situations. Write the null

27、 and alternative hypotheses for each example.i) You are interested in comparing the satisfaction rankings given by male and female purchasers of a new product.ii) You are interested in comparing the family incomes of purchasers of four different types of products.iii) You are interested in whether p

28、roduct ratings differ before and after use.(9 marks)i) Mann Whitneyii) Kruskal Wallisiii) WilcoxonQuestion 12A truck manufacturer keeps a log of diesel consumption of 20 trucks over a six-month period. From a previous study, the average consumption of trucks in Malaysia was found to be 4800 litres p

29、er month. He asks you to interpret the following results: Interpret the results obtained in Tables 10a and 10b. (5 marks)Ho: m = 4800 Ha: m 4800 m: mean diesel consumptionp-value 5%. Results are significant at the 5% sig. level. The average diesel consumption of trucks is significantly less than 480

30、0 (mean = 4215) . It can be seen that the average diesel consumption is 4215 litres per month (1m) between 3737.62 and 4692.35 litres per month (95% confidence interval for population mean). (1m)Question 13A researcher wishes to examine the effect of temperature on pilot performance. A random sample

31、 of 15 pilots was recorded following participation in an air stimulation task, in cockpits of differing temperatures (20 degrees Celsius and 35 degrees Celsius). A non-parametric test was conducted with the following results.Table 10Table 11(i) State the situation in which the non-parametric tests would have been suitable. (3 marks)(ii) What non-parametric test was used to generate Tables 10 and 11? (2 marks)(iii