Reference no: EM132515046
Q 1). A group of young businesswomen wish to open a high fashion boutique in a vacant store but only if the average income of households in the area is at least $25,000. A random sample of 9 households showed the following results. Assume the population of incomes is normally distributed. Test at 0.05 level of significance.
$28,000 $25,000 $27,000 $26,000 $22,000 $24,000 $26,000 $23,000 $24,000
Q 2). Insurance: In an insurance study of worker's deaths in a heavy mechanical complex of a country, monthly fatalities are analyzed for two different time periods. Sample data from the both time periods are summarized by the following statistics:
n1 = 12, x¯1 = 46.42, s1 = 11.07 n2 = 15, x¯2 = 51.06, s2 = 10.39
Q 3). (a). Suppose that we have a fuse box containing 20 fuses, of which 5 are defective. If two fuses are selected at random and removed from the box in succession without replacing the first, what is the probability that both are defective?
Q 3). (b). The probability that David solves a problem is 3/7 and the probability that Peterson solves the same problem is 7/15. Find the probability that:
a. At least one of them solves the problem.
b. Both of them solve the problem.
c. Neither of them solves the problem.
Q 4). (a). Textbooks: The college bookstore tells prospective students that the average cost of its textbooks is $52 with a standard deviation of $4.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore's claim against their alternative, the students select a random sample of size 100. Assume that the mean from their random sample is $52.80. Perform a hypothesis test at the 5% level of significance and state your decision.
Q 4) (b). Educational Program: A study has been conducted to examine the effectiveness of a new experimental program for preparing high school students for the SAT. Eighty students have been randomly divided into two groups of forty. One group receives the experimental program, and when they take the SAT the sample average score is equal to 1041.10 and the standard deviation of scores is 130.30. The second group receives a traditional program. They end up with an average score of 1012.48 with a standard deviation of 79.51. Does this result provide evidence that the new program is more effective than the traditional program? Test at 5% level of significance