Q1. The temperatures in chicken incubators on a chicken farm, measured in degrees Fahrenheit, are generally believed to have a variance of 0.50. The manager of the chicken farm claims that the variance has changed. He randomly tests 25 of his incubators and finds that their temperatures have a standard deviation of 0.55 degrees Fahrenheit. At the 0.05 level of significance, does this evidence support the manager's clam that the variance is not 0.50?
Q2. A college student is interested in investigating the claim that students who graduate with a master's devote earn higher salaries, on average, than those who finish with a bachelor's degree. She surveys, at random, 42 recent graduates who completed their master's degrees, and finds that their mean salary is $38,400 per year. The standard deviation of annual salaries for the population of recent graduates who have master's degrees is known to be S3100. She also surveys, at random 45 recent graduates who completed their bachelor's degrees and finds that their mean salary is $36,750 per year. The standard deviation of annual salaries for the Population of recent graduates with only bachelors' degrees is known to be $3700, Test the claim at the 0.05 level of significance.
Q3. A professor is concerned that the two sections of statistics that she teaches arc not performing at the same level. To test her claim, she looks at the mean exam score for a random sample of students from each of her classes. In Class 1, the mean exam score for 12 students is 78.7 with a standard deviation of 6.5. In class 2, the mean exam score for 15 students is 81.1 with a standard deviation of 7.4. Test the professor's claim at the 0.05 level of significance. Assume the population variances are equal.
Q4. An SAT prep course claims to Increase student scores by more than 60 points, on average. To test this claim, 9 students who have previously taken the SAT are randomly chosen to take the prep course. Their SAT scores before and after completing the prep course are listed on the following table. Test the claim at the 0.01 level of significance.
|
Before Prep
|
1010
|
980
|
1170
|
1200
|
1040
|
1280
|
1450
|
1470
|
1500
|
|
After Prep
|
1100
|
1260
|
1190
|
1280
|
1170
|
1370
|
1440
|
1500
|
1520
|
Q5. Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting .220 in a random sample of 50 at bats. For a random sample of 24 at bats since changing his training techniques, his batting average is .375. Determine if there is a sufficient evidence to say that his batting avenge has improved at the 0.10 level of significance. (NOTE: Even though the term average is used think of these in term of percent's or proportions)
Q6. A quality control inspector believes that the variance in the diameters of soda cans, measured in millimeters, is greater for soda cans produced by Machine A than for soda cans produced by Machine B. The sample variance of a random sample of 15 cans from Machine A is 2.788. The sample variance for a random sample of 17 soda cans from Machine B is 1.982. Test the inspector's claim using a 0.10 level of significance. Does the evidence support the inspector's claim?