3. QUESTION

CONSIDER THE FOLLOWING MULTIPLE-CHOICE QUESTIONS

CIRCLE YOUR SELECTION CLEARLY:

A certain brand of jelly beans are made so that each package contains about the same number of beans. The filling procedure is not perfect, however. The packages are filled with an average of 375 jelly beans, but the number going into each bag is normally distributed with a standard deviation of 8. Yesterday, Jane went to the store and purchased four of these packages in preparation for a Spring party. Jane was curious, and she counted the number of jelly beans in these packages - her four bags contained an average of 382 jelly beans. Student # : Surname & Initials : Page 8 of 10

In the above scenario, which of the following is a parameter?

a. The average number of jelly beans in Jane's packages, which is 382

b. The average number of jelly beans in Jane's packages, which is unknown

c. The average number of jelly beans in all packages made, which is 375

d. The average number of jelly beans in all packages made, which is unknown

If you went to the store and purchased six bags of this brand of jelly beans, what is the probability that the average number of jelly beans in your bags is less than 373?

a. 0.2709

b. 0.3085

c. 0.4013

d. 0.7291

Calculations:

According to the central limit theorem, what is the standard deviation of the sampling distribution of the sample mean?

a. The standard deviation of the population

b. The standard deviation of the sample

c. The standard deviation of the population divided by the square root of the sample size

d. The standard deviation of the sample divided by the square root of the sample size

\f1.2 Thembi was curious if sample maximum was an unbiased estimator of population maximum. She started with a large normally distributed population of test scores whose maximum was 99 points. She then took a random sample of 6 tests and calculated the maximum of the sample. She replaced those tests and repeated this process for a tota! of 40 trials. Her results are summarised in the dotplot beEow where each dot represents the maximum score from a sample of 6 tests '. I U I C II 0 i. III-III. I. III IIDOIIIIIIIDOIIIDC I l-H-l-H-H-l-I-H-I-l-H-I-m-I-I-I-l 75 80 35 QB 95 me Sample maximum nt if: Surname 8: Initials: Page 2 of 10 Based on these results, does the sample maximum appear to be a biased or unbiased estimator of population maximum. Hint : The population maximum is 99. Select an option below. a. Sample maximum appears to be a biased estimator since it consistently underestimated the population maximum b. Sample maximum appears to be a biased estimator since it consistently overestimated the population maximum :3. Sample maximum appears to be an unbiased estimator of the population maximum 1.3 Nomvuyo was curious if sample mean was an unbiased estimator of population mean. She placed ping pong balls numbered from 0 to 32 in a drum and mixed them well. Note that the population mean is 16. She then took a random sample of 5 balls and calculated the mean of the sample. She replaced the balls and repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each clot represents the sample mean from a sample of 5 balls l-I-I-H+|-|-H-|-H4-|+H-|-|-| 5 10 15 20 25 Sample mean Based on these results, does the sample mean appear to be a biased or unbiased estimator of population mean? Hint : The population mean is 16. Select an option below. a. Sample mean appears to be a biased estimator since it consistently underestimated the population mean b. Sample mean appears to be a biased estimator since it consistently overestimated the population mean c. Sample mean appears to be an unbiased estimator of the population mean