Mr. Raj, an investor, has narrowed his search for a mutual fund down to the Oppy fund or the MLPFS fund. Oppy’s rate of return is lower, but seems to be more stable than MLPFS’s. If Oppy’s variability in rate of return is signifi cantly lower than MLPFS’s, then he will invest his money there. If there is no signifi cant difference in variability, he’ll go with MLPFS. To make a decision, Mr. Raj has taken a sample of 21 monthly rates of return for both fi rms. For Oppy, the standard deviation was 2, and for MLPFS, the standard deviation was 3. Which fi rm should Mr. Raj invest in? Test at the α = 0.05 level.
An insurance company is interested in the length of hospital-stays for various illnesses. The company has randomly selected 20 patients from hospital A and 25 from hospital B who were treated for the same ailment. The amount of time spent in hospital A had an average of 2.4 days with a standard deviation of 0.6 day. The treatment time in hospital B averaged 2.3 days with a standard deviation of 0.9 day. Do patients at hospital A have signifi cantly less variability in their recovery time? Test at a 0.01 signifi cance level.
Nation’s Broadcasting Company is interested in the number of people who tune in to their hit shows Buddies and Ride to Nowhere; more importantly, the company is very concerned in the variability in the number of people who watch the shows. Advertisers want consistent viewers in hopes that consistent prolonged advertising will help to sell a product. Data are given below (in millions of viewers) for the past few months.
The HAL Corporation is about to unveil a new, faster personal computer, PAL, to replace its old model, CAL. Although PAL is faster than CAL on average, PAL’s processing speed seems more variable. (Processing speed depends on the program being run, the amount of input, and the amount of output.) Two samples of 25 runs, covering the range of jobs expected, were submitted to PAL and CAL (one sample to each). The results were as follows:
Two brand managers were in disagreement over the issue of whether urban homemakers had greater variability in grocery shopping patterns than did rural homemakers. To test their confl icting ideas, they took random samples of 70 homemakers from urban areas and 60 homemakers from rural areas. They found that the variance in days squared between shopping visits for urban homemakers was 14 and the sample variance for the rural homemakers was 3.5. Is the difference between the variances in days between shopping visits signifi cant at the 0.01 level?
Two competing ice cream stores, Yum-Yum and Goody, both advertise quarter-pound scoops of ice cream. There is some concern about the variability in the serving sizes, so two members of a local consumer group have sampled 25 scoops of Yum-Yum’s ice cream and 11 scoops of Goody’s. Of course, both members now have stomachaches, so you must help them out. Is there a difference in the variance of ice cream weights between Yum-Yum and Goody? The following data have been collected. Test at the 0.10 level.
The post office is concerned about the variability in the number of days it takes a letter to go from the east coast to the west coast. A sample of letters was mailed from the east coast, and the time taken for the letters to arrive at their address on the west coast was recorded. The following data were collected:
For the following contingency table, calculate the observed and expected frequencies and the chi-square statistic. State and test the appropriate hypotheses at the 0.05 signifi cance level.
Marketers know that tastes differ in various regions of the country. In the rental car business, an industry expert has given the opinion that there are strong regional preferences for size of car and quotes the following data in support of that view:
What probability distribution is used in each of these types of statistical tests? (a) Comparing two population proportions. (b) Value of a single population variance. (c) Comparing three or more population means. (d) Comparing two population means from small, dependent samples.
Minhajur Rahaman
