Read each carefully. show all computations. Answer all - points vary for each problem.

1) The data in the file below represent the cost per ounce, a sample of chocolate and macadamia nut bars.

2224251414247716141817111515161419191810

1. Construct 95% confidence interval for the population mean cost, per ounce in chocolate and macadamia nut bars.
2. Interpret the interval constructed in (a).
3. What assumptions must you make about the population distribution in order to construct the confidence interval estimated in (a)

2)Assume that you have a sample of n₁ = 9, with the sample mean X-Bar X₁ = 40, and a sample standard deviation of s₁ = 7, and you have an independent sample of n₂ = 11 from another population with a sample mean X-Bar X₂ = 36 and sample standard deviation s₂ = 8.

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 = 0.05, 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?

3) If a quality control manager want to estimate the mean life of light bulbs to within 21 hours with 95% confident and also assumes that the population standard deviation is 75 hours, how be selected.

4) The owner of a gasoline station wants to study gasoline purchasing habits by motorists at his station. He selects a random sample of 45 motorists during a certain week, with the following results:

• The amount purchased was X-Bar = 10.3 gallons, S = 3.3 gallons.
• 12 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 0.05 level of significance, is there evidence that fewer than 20% of all the motorists at the station purchased premium grade gasoline?