1. Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before after shortage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of 10 batches of a new cola recipe:
0.4 0.7 2.0 -0.4 2.2 -1.3 1.2 1.1 2.3 2.0
Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.
2. Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can read four paragraphs of text in the common Times New Roman font in an average time of 22 seconds. Researchers asked a random sample of 24 adults to read this text in the ornate font named Gigi. Here are their times, in seconds:
23.2 21.2 28.9 27.7 29.1 27.3 16.1 22.6 25.6 34.2 23.9 26.8
20.5 34.3 21.4 32.6 26.2 34.1 31.5 24.6 23.0 28.6 24.4 28.1
Do these data provide good evidence that the mean reading time for Gigi is greater than 22 seconds? Carry out an appropriate test to help you answer this question.
3. Great white sharks are big and hungry. Here are the lengths in feet of 44 great whites.
18.7 12.3 18.6 16.4 15.7 18.3 14.6 15.8 14.9 17.6 12.1
16.4 16.7 17.8 16.2 12.6 17.8 13.8 12.2 15.2 14.7 12.4
13.2 15.8 14.3 16.6 9.4 18.2 13.2 13.6 15.3 16.1 13.5
19.1 16.2 22.8 16.8 13.6 13.2 15.7 19.7 18.7 13.2 16.8
Construct and interpret a 95% confidence interval for the mean length of great white sharks. Based on this interval, is there significant evidence at the 5% level to reject the claim “Great white sharks average 20 feet in length”? Justify your answer.
4. A state’s Division of Motor Vehicles (DMV) claims that 60% of teens pass their driving test on the first attempt. An investigative reporter examines an SRS of the DMV records for 125 teens; 86 of them passed the test on their first try. Is this good evidence that the DMV’s claim is incorrect? Carry out a test at the = 0.05 significance level to help answer this question.
5. We hear that newborn babies are more likely to be boys than girls. Is this true? A random sample of 25,468 firstborn children included 13,173 boys. Boys do make up more than half of the sample, but of course we don’t expect a perfect 50-50 split in a random sample.
Do these data give convincing evidence that boys are more common than girls in the population? Carry out a significance test to help answer this question.