Exercise 3. C & D and Exercise 5 (complete just as Ex 4 using original numbers. You can take a picture or scan and upload for grading.SampleFinaljuly21.doc

Read each carefully. Please show all computations. Answer all – points vary for each.

1. The data in the file represent egg and cheese symbolizes the total fat, in grams per serving, for a sample of 20 egg and cheese sandwiches from a fast-food restaurant. The data are as follows:

7 8 3 5 15 21 22 24 18 33

23 31 25 19 29 29 29 30 41 55

a) Find the mean, mode and the median.

b) Construct 95% confidence interval for the population mean total fat, in grams preserving.

c) Interpret the interval constructed in (a).

d) What assumptions must you make about the population distribution in order to construct the confidence interval estimate in (a)

2. If a quality control manager wants to estimate the mean life of light bulbs to within + 21 hours with 99% confidence and also assumes that the population standard deviation is 85 hours, how many light bulbs needed to be selected?

3. The owner of a gasoline station wants to study gasoline purchasing habits by motorists at his station. He selects a random sample of 55 motorists during a certain week, with the following results:

· The amount purchased was XBar = 11.0 gallons, S = 3.3 gallons.

· 15 motorists purchased premium-grade gasoline.

a. At the 0.05 level of significance, is there evidence that the population mean purchase was different from 10 gallons?

b. At the 0.10 level of significance, is there evidence that fewer than 25% of all the motorists at the station purchased premium grade gasoline?

c. What is your answer to (a) if the sample mean equals 11.3 gallons?

d. What is your answer to (c)if 7 motorists purchased premium gasoline?

4. Assume that you have a sample of n1 = 7, with the sample mean XBar X1 = 44, and a sample standard deviation of S1 = 5, and you have an independent sample of n2 = 14 from another population with a sample mean XBar X2 = 36 and sample standard deviation S2 = 6.

a. What is the value of the pooled-variance tSTAT test statistic for testing H0:µ1 = µ2?

b. In finding the critical value ta/2, how many degrees of freedom are there?

c. Using the level of significance α = 0.01, what is the critical value for a one tail test of the hypothesis H0:µ1 ≤ µ2 against the alternative H1:µ1 > µ2?

d. What is your statistical decision?

e. Referring to problem 4, if n1 = 4 and n2 = 3, how many degrees of freedom do you have? Also referring to problem 4, n1 = 4 and n2 = 3,

a. what is the value of the pooled-variance tSTAT test statistic for testing H0:µ1 = µ2?

b. In finding the critical value ta/2, how many degrees of freedom are there?

c. Using at the 0.01 level of significance, what is the critical value for a two tail test and is there evidence that µ1 > µ2?

d. What is your statistical decision?

That’s all folks

Have a great season!

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