Question

Conduct a hypothesis test for each problem, using the traditional method. Show the 5 steps and all work for each hypothesis test. Be sure you select the correct test to use for each problem.

1. A telephone company claims that less than 30% of all college students have a limited number of text messages per month. A random sample of 150 students revealed that 41 of them have a limited number. Test the company's claim at the 0.01 level of significance.

2. A college statistics instructor claims that the mean age of college statistics students is 25. A random sample of 98 college statistics students revealed a mean age of 23.1. The population standard deviation is known to be 3.21 years. Test his claim at the 0.05 level of significance.

3. A random sample of 113 adults ages 18-24 showed that 27 had donated blood within the past year, while a random sample of 166 adults who were at least 25 years old had 48 people who had donated blood within the past year. At the 0.10 level of significance, test the claim that the proportion of blood donors is equal for these two age groups.

4. A librarian claims that the mean number of books read per month by community college students is less than 2.5 books. A random sample of 30 community college students had read a mean of 1.73 books with a standard deviation of 2.14 books. Test the librarian's claim at the 0.05 level of significance.

5. A reading group claims that Americans read more as they grow older. A random sample of 65 Americans age 60 or older read for a mean length of 63.8 minutes per day, with a population standard deviation of 15.5 minutes per day. A random sample of 88 Americans between the ages of 50 and 59 read for a mean length of 56.2 minutes per day, with a population standard deviation of 23.1 minutes per day. At the 0.01 level of significance, test the claim that the mean time spent reading per day by Americans age 60 and older is longer than the mean time spent reading per day by Americans between the ages of 50 and 59.

6. A car manufacturer advertises that a certain model has a variance in miles per gallon equal to 12.25. A car magazine wanted to check the advertisement and collected a random sample of 15 cars to test and found the variance in miles per gallon equal to 17.64. At the 0.1 level of significance, test the magazine's claim that the variance is different from 3.5 miles.

Answer 1

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