Need explanation with all answer:

Question 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 1929 29 29 30 41 55

1. Find the mean, mode and the median.
2. Construct 95% confidence interval for the population mean total fat, in grams preserving.
3. Interpret the interval constructed in (a).
4. What assumptions must you make about the population distribution in order to construct the confidence interval estimate in (a)

Question 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?

Question 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.

1. At the 0.05 level of significance, is there evidence that the population mean purchase was different from 10 gallons?
2. At the 0.1O level of significance, is there evidence that fewer than 25% of all the motorists at the station purchased premium grade gasoline?
3. What is your answer to (a) if the sample mean equals 11.3 gallons?
4. What is your answer to (c)if 7 motorists purchased premium gasoline?

Question 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.

1. What is the value of the pooled-variance t_STAT test statistic for testing H₀:₁= ₂?
2. In finding the critical value t_a/2, how many degrees of freedom are there?
3. Using the level of significance = 0.01, what is the critical value for a one tail test of the hypothesis H₀:_{1 2} against the alternative H₁:₁> ₂?
4. What is your statistical decision?

Question 5. 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, at the 0.10 level of significance, what is the critical value for a two tail test and is there evidence that ₁> ₂?

Question 6. If you want to be 99% confident of estimating the population proportion to within a sampling error of {0.04, what sample size is needed?

Question 7. If the inspection division of a county weights and measures department wants to estimate the mean amount of soft-drink fill in 2-liter bottles to within {0.01 liter with 95% confidence and also assumes that the standard deviation is 0.05 liter, what sample size is needed?