Question

3 The manufacturer of Ice Melt claims that its product will melt snow ani KZ temperatures as low as O" Celsius. A representative for a large chain of hardware stores is interested in testing this claim. The chain purchases a large shipment of s kilo bags for distribution. The representative wants to know, with 95%cofdene and within :005 degrees, whal proportion of bugs of le Melt perfoum the jpb a claimed by the manu facturer. (15 points) a. How many bags does the representative need to tear? What assumption ahould be made concerning the population proportion? (5 points) b. Suppose that the representative tests 50 bugs, and 42 of them do the job as claimed Construct a 99% confidence interval estimate for thepopulation proportion that will do the job as claimed. (5 points) c. How can the representative use the results of (b) to determine whether to sell the Ice Melt product? (5 polnts) 4. Ahmad and Alia, the owners of an upscale restaurant in Tunis, want to sudy the dining characteristics of their customers. They decide to focus on two variables the amount of money spent by customers and whether customers order dosert. The results from a sample of 36 customers are as follows: Amount spent X-TND 38 54 S TND 7.26, and 18 customers purchased dessert (25 points) Construct a 90% confidence interval estimate for the population mean amount spent per customer in the restaurant. (5 points) b. Construct a 95% nfidence interval est mate for the population proportion of customers who purchase dessert. (5 points) Fatma, the owner of a competing restaurant, wants to conduct a similar survey in her restaurant She does not have access to the information that Ali and Alia have obtained from the survey they conducted. Answer the following questions c. What sample size is needed to have 99% confidence ofestmtng the population mean amount spent in her restaurant to within TND 15, assuming that the standard deviation is est imated to be TND 8? (5 points) d. How many customers need to be selected to have 90% confidence of estimuting the population proportion of customers who purchase dessert to within +0.04.(5 points) e Based on your answers to te) and (d), how burge a samplesld Fatuke" S points)

Answer 1

3a:

Since no estimate of population proportion is given so let $hat{p}=0.5$

The critical value of z for 95% confidence interval is .

The margin of error E= 0.05, so required sample size will be

So required sample size for 95% confidence interval is 385.

b:

Sample proportion is

For 99% confidence interval, using excel function "=NORMSINV(0.995)", critical value of z will be

Confidence interval for population proportion will be

c:

We are 99% confident that the product is success between 71% and 97% times. So it seems to be good product.