1. A sample of seed packets was selected, and their weights in grams were recorded as follows: 15.1, 15.6, 15.8, 15.1, 15.5, 15.9, 15.5, 15.2. Determine a 90% confidence interval for the mean weight of seeds in all packets.
2. A manufacturer of passenger car tires claims that the lifetime of its tires is at least 30,000 miles. A consumer testing bureau tests this claim at a significance level of 1% with a sample of 45 tires. The sample statistics are as follows: the mean is 29,560,and the standard deviation is 1,430.What is the appropriate conclusion?
3. A car insurance company claims that the average annual rates of $1075 have not increased over the last three years. A sample of 18 customers showed a mean of $1735 and a standard deviation of $222. The test claim at a 5% significance level.
4. To determine whether the intake of a certain nutrient, in grams, is significantly less in one group than in another, samples were taken and the following statistics obtained: Group 1, x1 = 66.3, s1= 9.17, n1 = 15 and Group 2, x2 = 77.8, s2 = 11.34, n2 = 10. At a 1% significance level, do the data indicate that individuals in group 2 take in a greater amount of nutrient than those in group 1? Assume the criteria for using the pooled t-test are satisfied.
The solution gives the details of student t test for comparing mean. Construction of confidence interval is also discussed in detail.