1.An insurance company states that 90% of its claims are settled with 5 weeks. A consumer group selected a random sample of 100 of the company's claims and found 75 of the claims were settled within 5 weeks. Is there enough evidence to support the consumer group's claim that fewer that fewer than 90% of the claims were settled within 5 weeks? Test using the traditional approach with alpha= 0.05.
2.A random sample of 51 observations was selected from a normally distributed population. The sample mean was xbar = 88.6, and the sample variance was s^2 = 38.2. does the sample show sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance? Use the p-value method.
3. A researcher wishes to compare two different groups of students with respect to their mean time to complete a particular task. The time required is determined for each group. The data summary is given below. Test the claim at alpha = 0.05, that there is no variance. Give the critical region, test statistic value, and conclusion for the F test.
4. The number of sit-ups that a person can do in one minute, both before and after a physical fitness course was recorded. The data is shown below for 10 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place: Assume variable is normally distributed. Test using alpha = 0.01
Before 30 23 25 29 27 25 30 45 34 26
After 31 27 25 35 34 35 32 52 50 43
5.You are given the following data. Test the claim that there is a difference in the means of the two groups. Use alpha = 0.10
Group A Group B
xbar1 =2 xbar2 =1.7
s1 =0.6 s2 = 0.7
n1 =120 n2 = 34
This solution addresses concepts of traditional statistical analysis, p-value method, F-testing and testing differences. All steps are shown enclosed in an Excel file.