A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two- year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Of the 35 two-year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Test the student's claim at the 0.10 significance level. a) The null and alternative hypothesis would be: O Ho: µp = PT H1:µp < PT O Ho: PF PT H1:PF < PT O Ho:µF = HT H1:µp > PT O Ho: HF HT H1:µF + HT O Ho: PF PT H1:pF > PT %3D O Ho:PF = PT H1:PF + PT b) Determine the test statistic. Round to two decimals. t = c) Find the p-value and round to 4 decimals. d) Make a decision. O Fail to reject the null hypothesis O Reject the null hypothesis e) Write the conclusion. O There is not sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college. O There is sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college.

Almost all medical schools in the United States require applicants to take the Medical College Admission Test (MCAT). On one exam, the scores of all applicants on the biological sciences part of the MCAT were approximately Normal with mean 9.5 and standard deviation 2.4. For applicants who actually entered medical school, the mean score was 10.8 and the standard deviation was 1.8. (a) What percent of all applicants had scores higher than 11? ANSWER: % (b) What percent of those who entered medical school had scores between 9 and 12? ANSWER: %

The speed of cars  on a specific road is normally distributed with a mean of 54 mph and a standard deviation of 3. The top 2.5% of cars are traveling at at least what mph?

Average adult Americans are about one inch taller but nearly a whopping 25 pounds heavier than they were in 1960, according to a report from the Centers for Disease Control and Prevention (CDC).  City A is considered one of America's healthiest cities.  Is the weight gain since 1960 similar in city A? A sample of n=25 adults suggested a mean increase of 22 pounds with a standard deviation of 9.4 pounds.  Is City A significantly different in terms of weight gain since 1960? Complete and interpret 5 step hypothesis testing by hand at a 5% level of significance using a Z-test.  Show each step and your work.

An IQ test has a mean of 96 and a standard deviation of 15. Which is more​ unusual, an IQ of 81 or an IQ of 120​?

An instructor claims that the average number of hours needed to study for a final exam in order to pass should be 5 hours. A student believes that the instructor is understating the number of hours needed to pass and surveys 36 students and finds the sample mean and standard deviation to be 5.7  and 1.5 hours respectively.  Test the instructors claim at a .10 level.

The average expenditure on Valentine's Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 46 male consumers was $132.31, and the average expenditure in a sample survey of 37 female consumers was $63.58. Based on past surveys, the standard deviation for male consumers is assumed to be $33, and the standard deviation for female consumers is assumed to be $20. The z value is 2.576. Round your answers to 2 decimal places. a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females? b. At 99% confidence, what is the margin of error? c. Develop a 99% confidence interval for the difference between the two population means. to

Assume that adults have IQ scores that are normally distributed with a mean of 96 and a standard deviation 19.3. Find the first quartile Q1,which is the IQ score separating the bottom 25% from the top 75%. The first quartile is?

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1469 and a standard deviation of 296. The local college includes a minimum score of 1824 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement?

The mean SAT verbal score is 485​, with a standard deviation of 97. Use the empirical rule to determine what percent of the scores lie between 485 and 679. ​(Assume the data set has a​ bell-shaped distribution.)