10.2 Warm Up

At a manufacturing company for medical supplies, machines produce parts used in highly specialized lasers. Company researchers are testing a new machine designed to improve the precision of the parts. The null hypothesis is that the new machine does not improve the precision. For the researchers, the more consequential error would be that the new machine actually improves the precision, but the test does not detect the improvement. Which of the following should the researchers do to avoid the more consequential error?

• Increase the significance level to increase the probability of a Type I error.

• Increase the significance level to decrease the probability of a Type I error.

• Decrease the significance level to increase the probability of a Type I error.

• Decrease the significance level to decrease the probability of a Type I error.

• Decrease the significance level to decrease the standard error.

Answer explanation

• The p-value is less than α, and the null hypothesis is rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

• The p-value is less than α, and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

• The p-value is less than α, and the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

• The p-value is greater than α, and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

• The p-value is greater than α, and the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

Data will be collected on the following variables. Which variable is most likely to be approximated by a normal model?

• The distribution of life span, in minutes, for batteries of a certain size, where most life spans cluster around the center of the distribution but with some very low and some very high life spans

• The distribution of ages, in years, of the students at a certain college, where most students are between 18 and 22 years old, but ages greater than 22 will probably be more spread out than ages less than 18

• The distribution of the number of birthdays per month for the employees at a certain company, where the number of birthdays in each month is approximately equal

• The distribution of the length of a stay, in days, in a hospital after surgery, where many patients have very short hospital stays, but some stays are quite lengthy and considered high outliers

• The distribution of the number of books read last week by middle school students, where the right tail of the distribution is longer than the left.

A city has designed a survey to collect information about residents’ opinions about city services. Which of the following describes a scenario in which nonresponse bias is likely present?

• Surveys were mailed to 500 people, and 200 of the surveys were completed and returned.

• Surveys were mailed to one-half of the neighborhoods in the city and all surveys were returned.

• Surveys were completed by the first 500 residents who listened to a radio show.

• Surveys were completed by 500 residents selected at random.

• Surveys were given to all residents in one neighborhood of the city and all surveys were returned.

The statistic x̄ is used as an estimator for which of the following?

• n

• s

• σ

• μ

• z