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2.  About 13% of the United States population is left-handed.  Suppose that a researcher speculates that individuals with schizophrenia are more likely to be left-handed than the US population.  The researcher surveys 104 individuals with schizophrenia and finds that 22 of them are left-handed.  Based on this sample, is there enough evidence that the population proportion of individuals with schizophrenia who are left-handed is more than the 13% (or 0.13).  (While answering the following sub-parts of this question, you will be including the null and alternative hypothesis, the test statistic, the p-value (a visualization and an interpretation), your statistical decision, and your conclusion in the context of the problem.) (c) Interpret the p-value for Step 3 of the hypothesis test.

2.  About 13% of the United States population is left-handed.  Suppose that a researcher speculates that individuals with schizophrenia are more likely to be left-handed than the US population.  The researcher surveys 104 individuals with schizophrenia and finds that 22 of them are left-handed.  Based on this sample, is there enough evidence that the population proportion of individuals with schizophrenia who are left-handed is more than the 13% (or 0.13).  (While answering the following sub-parts of this question, you will be including the null and alternative hypothesis, the test statistic, the p-value (a visualization and an interpretation), your statistical decision, and your conclusion in the context of the problem.) (a) Which of the following best represents the hypothesis for Step 1 of the hypothesis test?

4. Are men less likely to retire by age 60 than women?  A study was conducted in which 350 men and 350 women were randomly selected to find the proportion of men and women who retired by age 60.  Of the 350 men, 179 retired by age 60.  Of the 350 women, 213 retired by age 60.  The following table displays the data for these two groups. Group n Number who retire by age 60 Males 350 179 Females 350 213 Test the research hypothesis that the population proportion of men who retire by age 60 is less than women who retire by age 60.  (While answering the following sub-parts of this question, you will be including the null and alternative hypothesis, the test statistic, the p-value (a visualization and an interpretation), your statistical decision, and your conclusion in the context of the problem.) (a) What type of hypothesis test is this (think Step 1)?

1.  In 2005-06 the average cost of tuition and fees at private four-year colleges was reported at just over $21,000 per year (www.collegeboard.com, October 18th, 2005).  More specifically, the population average cost of tuition and fees for private four-year colleges is $21,325 and the standard deviation is $23,952.  Assume that a random sample of 25 private four-year colleges will be selected. (d)  What is the probability that the sample mean tuition and fees for the 25 private four-year colleges will be more than $25,000?

3.  About 13% of the United States population is left-handed.  Suppose that a researcher speculates that individuals with schizophrenia are more likely to be left-handed than the US population.  The researcher surveys 104 individuals with schizophrenia and finds that 22 of them are left-handed.  Based on this sample, is there enough evidence that the population proportion of individuals with schizophrenia who are left-handed is more than the 13% (or 0.13).  Construct and interpret a 95% confidence interval for the population proportion of individuals with schizophrenia who are left-handed. (b) What is the sample size (n) for the confidence interval?

8.  A survey was given to SF students during the Summer A 2026 semester to determine natural hair color.  The table below gives the probability that a randomly chosen student has a particular hair color. Hair Color Brown Blonde Black Red Other Probability 0.47 ?? 0.33 0.03 0.10 (b) Find the probability that a student has brown or blonde hair.

7.  A survey suggests that 13% of students vape daily, while 68% exercise regularly.  Furthermore, 5% of students vape daily and exercise regularly.  Based on this given information, fill in the remaining boxes of the following table (boxes labeled a, b, c, d, e and f). Note:  based on some information above, some boxes have been filled in for you. Do you vape daily? Yes No Totals Do you exercise regularly? Yes (a) (b) 68% No (c) (d) (e) Totals 13% (f) 100%   (g) What is the probability that a student vapes daily or exercises regularly?

5.  Is the number of games won by a major league baseball team in a season related to how many runs the team scored for the season?  The table below shows the runs scored (x) and the number of games won (y) for a sample of teams from the 2025 season. X (Runs Scored)    849    798    825    806    793 Y (Number of Games Won)    94    94    93    97    92 Find the equation of the regression line using the least squares approach.  You may use the results of your calculator’s LinReg procedure. (b) What is the name of b1 ? 

6. Each year seasoned mountaineers as well as many novice climbers looking for a once in a lifetime experience attempt the hardest endurance climb in the lower 48 states.  The glaciated peek of Mt. Rainier, located outside of Seattle Washington, stands at 14,411 feet.  From one of the more popular high camps, Camp Muir at 10,100’, climbers start their 8-12 hour push for the summit in the early morning hours (between 1am and 4am), climbing in the darkness by the light of their headlamps.  A study was conducted to see if the length of time to run 5 miles at sea level could be used to predict the length of time to reach the summit.  A random sample of 17 mountaineers was selected and data on the length of time (in minutes) to run 5 miles (x) and the length of time (in hours) to reach the summit (y) was used to fit a straight-line model.  The results of the simple linear regression are provided below. (a) Calculate the coefficient of determination (R2).   (Round your answer to four decimal places.)

13.  Consider the following discrete probability distribution. X 3 5 7 9 11 P(X) 0.5 0.2 0.1 0.1 0.1 (c)  Find the mean of this discrete probability distribution.  (Round your answer to one decimal place).