Discuss the following:
Q1. A medical school claims that more than 28% of its students plan to go into general practice.
a. It is found that among a random sample of 130 of the school's students, 42 of them plan to go into general practice. Does this sample evidence support the school's claim? Use the p-value approach and a = 0.05 to make your decision.
b. Suppose a second sample is collected a year after the first with the results indicating 57 out of 135 plan to go into general practice. Does this sample evidence support the school's claim? Use the p-value approach and a = 0.05 to make your decision.
Q2. The health of employees is monitored by periodically weighing them. A sample of 54 employees has a mean weight of 183.9 lbs. Assuming that s is known to be 121.2 lb. Use a 0.10 level to test the claim that the population mean weight of all such employees is less than 200 lb.
Q3. A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is not 30 g and wants to verify that the product is meeting specifications. The mean weight for a random sample of 16 ball bearings is 29.5 g with a standard deviation of 4.1 g. At the 0.05 significance level, test the claim that the mean is not 30 g. You may assume the weights are normally distributed.
Q4. In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures.
518
548
561
523
536
499
538
557
528
563
a. Find x-bar and s for this data set.
b. At the 5% significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours? You may assume the times between failures are normally distributed. Use the traditional method to make your decision.
Q5. A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below.
14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2
At the 0.01 significance level, does the sample support the company's claim that the mean weight is at least 14 ounces? You may assume the weight of cereal packets is normally distributed.
Q6. Various temperature measurements are recorded at different times for a particular city. The mean of 21°C is obtained for 32 temperatures on 32 different days. Assuming that σ = 1.5°C, test the claim that the population mean is actually less than 22°C. Use a 0.05 significance level.