= 22pt

Math 3310 --- Exam I
September 14, 2000

(12 pts) 1. In order for a computer hard drive to function properly, the length of a criticial component must have a standard deviation of less than 0.15 mm. We examine 30 of these components and find a sample standard deviation of 013 mm. Test the claim that the standard deviation is less than 0.15 mm. Let a = .05.

(10 pts) 2. A national computer retailer believes that average sales are greater for salespersons with a college degree. The retailer randomnly samples salespeople from each group. Here are the results:

Degreed: Group 1	Non-degreed: Group 2
n₁ = 34	n₂ = 37
x₁ = 3542.00	x₂ = 3301.00
s₁ = 468	s₂ = 642

Find a 95% Confidence Interval for (µ₁ - µ₂).

(8 pts) 3. As part of its fund-raising program, a civic organization sells an energy saving light bulb that it claims has an average life of more than 3200 hours. A sample of 8 light bulbs was tested and the sample mean was x = 3503 hours, with a sample standard deviation of s = 351.6 hours. Test the claim that the bulbs have an average life of more than 3200 hours. Let a = .05.

(4 pts) 4. A statistics department has found that, in the past, the average grade on the final exam for its introductory course is 74.8, and the standard deviation is 8.2. Suppose a class of 32 people are currently taking the course. Find the probability that their average score will fall between 72.8 and 76.8.

(10 pts) 5. A vitamin company manufactures 1000 mg oyster shell calcium tablets. Seventy-one tablets were randomly selected from a production run, and each tablet was analyzed for its calcium content. The sample mean was 1002.8 mg and the sample standard deviation was 3.4 mg.
a. Find a 98% Confidence Interval for s².
b. Find a 98% Confidence Interval for s.

(6 pts) 6. Suppose we conducted an experiment in which H₀: µ ³ 55, H₁: µ < 55, Z^* = -2.64, n = 43, and a = 0.01.
a. Calculate the p value.
b. Based on your result from Part a, would you reject or fail to reject H₀?

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