A credit score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. Values range from 300 to 850 , with a credit score over 700 considered to be a quality credit risk. According to a survery, the mean credit score is 706.1 . A credit analyst wondered whether high-income individuals (incomes in excess of \( \$ 100,000 \) per year) had higher credit scores. He obtained a random sample of 45 high-income individuals and found the sample mean credit score to be 719.6 with a standard deviation of 84.2 . Conduct the appropriate test to determine if high-income individuals have higher credit scores at the \( \alpha=0.05 \) level of significance. a click the icon to view the table of critical t-values. Approximate the P-value.

The five-number summary for a data set is: Min \( =14 \quad Q_{1}=40 \quad M=55 \quad Q_{3}=62 \quad \) Max \( =99 \) a Determine the values of the upper and lower fences. b The smallest three values in the data set are \( 6,18,34 \) and the largest are \( 90,94,99 \). Which of these are outliers?

a) Find the critical \( \chi^{2}- \) value for a left-tailed test when \( n=11 \) and \( \alpha=0.01 \). marks] b) Find the critical \( \chi^{2}- \) value for a two-tailed test when \( n=9 \) and \( \alpha=0.05 \). marks]

Construct a box plot from the given data. Diameters of Cans in an Assembly Line: \( 5.8,5.7,5.2,5.5,5.3,5.7,5.8,5.4,5.9,5.3 \)

Scores on a test have a mean of 78 and a standard deviation of 13 . Tom has a score of 66 . Convert Tom's score to a \( z \)-score, rounded to the nearest hundredth.

A water bottling facility has a mean bottling rate of 33.5 thousand bottles per hour with a standard deviation of 1.92 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 26.2 thousand bottles per hour with a standard deviation of 1.42 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 36.8 thousand bottles of water, and the cola bottling facility bottled 28.4 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer