Question 1) Seventy data clerks at large manufacturing Co. make average of 27 errors per day normally distributed with the standard deviation of 4. An auditor can check work of 22 clerks per day. Find the probability that the average number of errors in a group of 22 clerks checked on one day is:
i) Fewer than 25?
ii) Greater than 30?
(b) Sui northern gas has find out that cost per 100 sq ft for the residential population electrical service is Rs.3.50 on average, with standard deviation of Rs.0.60. Two different samples are chosen at random, and means are Rs. 3.10 and Rs.3.80 respectively. Assistant in charge of data collection concludes that the second sample is the better one because it is better to overestimate than underestimate the true mean. Explain. Is one of the means “better” in some ways, given the true population mean?
Question 2) A graduate students has just completed first draft of his 700 page dissertation. He has typed his paper himself and is interested in knowing average number of typographical errors per page, but doesn’t want to read the whole paper. Knowing a little bit about business statistics, he selected 40 pages at random to read and found that the average number of typos per page was 4.3 and the sample standard deviation was 1.2 typos per page.
(a) Compute the estimated standard error of the mean.
(b) Construct a 90 percent confidence interval for the true average number of typos per page in his paper.
Question 3) University bookstore is facing noteworthy competition from off-campus bookstores, and they are considering targeting a specific class in order to retain student business. Bookstore randomly sampled 150 freshmen and 175 sophomores. They found that 46 percent of freshmen and 40 percent of sophomores purchase all of their textbooks at the university bookstore. At α = 0.10, is there a major difference in the proportions of freshman and sophomores who purchase completely at the university bookstore?
Question 4) Mecca Cola is studying the effect of its latest advertising campaign. People selected at random where called and asked how many cans of Mecca cola they had bought in past week and how many Mecca Cola advertisements they had either read or seen in the past week.
X (number of ads) 3 7 4 2 0 4 1 2
Y (cans purchased) 11 18 9 4 7 6 3 8
(a) Develop the estimating equation that best fits the data
(b) Compute the sample coefficient of determination and the sample coefficient of correlation.
Question 5) A foods company has added broiled whole chickens to its line of takeout food for busy professionals who do not have time to cook at home. The number of precooked chickens sold in the first 7 weeks is:
Week 1 2 3 4 5 6 7
Sales 41 52 79 76 72 59 41
(a) Determine the linear regression line that best fits these data
(b) Calculate the expected number of sales for week 8
(c) Based on the estimate in part (b) and the available data, does the regression accurately explain the sales trend for this item?