3.2 Which of the following are statistics, and which of the following are parameters?

a.The mean height of a sample of basketball players in the National Basketball Association.

b.The mean weight of the population of football players on the Washington Redskin team

c.The mean blood pressure of the population of patients in the cardiac ward of a hospital

d.The mean blood grade of students in a certain elementary algebra section at a college, which is used to estimate the mean grade of all students in all sections of elementary algebra at the college.

From a random sample of

77

students in an introductory finance class that uses​ group-learning techniques, the mean examination score was found to be

76.3476.34

and the sample standard deviation was

2.32.3.

For an independent random sample of

88

students in another introductory finance class that does not use​ group-learning techniques, the sample mean and standard deviation of exam scores were

70.7270.72

and

8.88.8​,

respectively. Estimate with

9090​%

confidence the difference between the two population mean​ scores; do not assume equal population variances.

The time needed for college students to complete a certain puzzle is modelled using a normal distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the
population mean time µ is changed by vigorous exercise, so you have a group of nine college students
exercise vigorously for 30 minutes and then complete the puzzle. What is the rejection region at the
significance level 0.01?
What is the power of the test at µ = 28 and σ = 1 in the above question?

2. According to survey data collected from 500 students in a recent Statistics class, the histogram for the number of hours of sleep they typically got per night is close to the normal curve with an average of 6.5 hours and a SD of 1.4 hours.

a) Find percentage of students who sleep between 7 and 8 hours

b) A student who sleeps 7 hours per night is at the _______th percentile of the score distribution

c) Find the first quartile of the sleep time and explain your result.

Sixty college students were asked where they shop online to determine on which websites the college should place advertisements. The data from the random sample of students is represented below. They compared Etsy, Amazon, and Ebay. Test at the .05 level of significance.

What are your null and alternative hypotheses?

What is the critical value?

What is your decision?

Reject the Null

Fail to Reject the Null

What is your interpretation of the following (ie. conclusion)?

At one liberal arts​ college, students are classified as humanities​ majors, science​ majors, or undecided. The chances are 36​% that a humanities major will change to a science major from one year to the​ next, and 17​% that a humanities major will change to undecided. A science major will change to humanities with probability 0.31​, and to undecided with probability 0.34. An undecided will switch to humanities or science with probabilities of 0.31 and 0.23​, respectively. Find the​ long-range prediction for the fraction of students in each of these three majors. The​ long-range prediction is humanities, ​science, undecided.

In 2015, the student body of Lock Haven University consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The calculated value for the test statistic equals?

The president of a university claims that the mean time spent partying by all students at this university is not more than 7 hours per week. A random sample of 30 students taken from this university showed that they spent an average of 9.50 hours partying the previous week with a standard deviation of 2.3 hours. Test at a significance level of 0.025 whether the president’s claim is true.

1. Write the null and the alternative hypothesis.
2. Calculate the test statistics.
3. Obtain the p-value.
4. Give your conclusion.

The composite scores of individual students on the ACT college entrance examination in 2009 followed a normal distribution with mean 21.1 and standard deviation 5.1.

1. What is the probability that a single student randomly chosen from all those taking the test scores 23 or higher?
   P( X >__?__ ) = P(z >__?__ ) = ____?__
2. 
   
3. What is the probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher?
   P( X̄ >_?__ ) = P(z >___?__ ) = ___?____

In a school district, all sixth grade students take the same standardized test. The superintendent of the school district takes a random sample of 26 scores from all of the students who took the test. She sees that the mean score is 130 with a standard deviation of 7.2344. The superintendent wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 16. Is there evidence that the standard deviation of test scores has decreased at the α = 0.05 level? Assume the population is normally distributed.