One research study of illegal drug use among​ 12- to​ 17-year-olds reported a decrease in use​ (from 11.4% in​ 1997) to 9.9​% now. Suppose a survey in a large high school reveals​ that, in a random sample of 1 comma 047 ​students, 94 report using illegal drugs. Use a 0.05 significance level to test the​ principal's claim that illegal drug use in her school is below the current national average.

Formulate the null and alternative hypotheses. Choose the correct answer below.

Find the test statistic. z=__

Find the P-Value. P-value =

The belief is that the mean number of hours per week of part-time work of high school seniors in a city is 10.4 hours. Data from a simple random sample of 28 high school seniors indicated that their mean number of part-time work was 11.5 with a standard deviation of 1.3. Test whether these data cast doubt on the current belief. (use α = 0.05) 1.) State your null and alternative hypotheses.

2.) State the rejection region.

3.) Calculate the test statistic.

4.) Determine the P-value for your test.

5.) State your conclusion for your hypothesis test.

Suppose that a principal of a local high school tracks the number of minutes his students spend texting on a given school day. He finds that the distribution of minutes spent texting is roughly normal with a mean of 60 and a standard deviation of 20. Use this information to answer the following questions.

1. Based on the statistics, find the two numbers of minutes that define the middle 95% of students in the distribution. What is the value for the lower number that you found?

2. Based on the statistics, find the two numbers of minutes that define the middle 95% of students in the distribution. What is the value for the higher number that you found?

The CDC estimates that 20% of people in the US between the ages of 15 and 24 have an STI. Suppose we do a test at a local college campus and find that 11 out of 117 people tested have an STI. Is this random variation or does this school have a lower than average level of infection?

• What test should we perform and why?
• What is your null and alternative hypothesis?
• Perform the test. What is the test statistic and what is the p value?
• What is your conclusion? Based on the data above, does this school have a higher than average level of infection or is this random variation?

Mr. S. P. Johnson is creating a college fund for his daughter. He plans to make 7-yearly payments of $10,000 each with the first payment deposited today on his daughter’s 6th birthday (happy birthday!) Assuming his daughter will need three equal withdrawals from this account to pay for her law-school education beginning when she is twenty-two (i.e. 22, 23, 24), how much will she have on a yearly basis for her law school career? Mr. Johnson expects to earn a constant 10% annual return for the time interval of this problem.

2. The long-term graduation rate for female athletes at a certain midwestern university is 72%. A random sample of female athletes at this school over the past few years showed that 29 of 35 females athletes graduated.

   (a) (10 pts) Test to determine if the proportion of female athletes who graduate from this school is greater than 72% at the 0.05 level of significance.

   (b) (5 pts) Suppose that a Type I error was made in the hypothesis test in part (a). Explain what a Type I error would be in the context of this problem. What is the probability of committing a Type I error in this problem?

An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 89 students in the school. There are 41 in the Spanish class, 31 in the French class, and 22 in the German class. There are 15 students that in both Spanish and French, 7 are in both Spanish and German, and 9 are in both French and German. In addition, there are 4 students taking all 3 classes.

If one student is chosen randomly, what is the probability that he or she is taking at least one language class?

If two students are chosen randomly, what is the probability that neither of them is taking a language class?

1. At a Midwestern University the 386 students in the Business School were classified according to their major within the business school and their gender. The results follow.

1. Find the probability that the selected student is a finance major and a male.

b. Find the probability that the selected student is an administration major or a finance major.

c. Find the probability that the selected student is an administration major or a female.

d. Find the probability that the selected student is finance major, given he is a male.

* Make sure you turn in your code (take a screen shot of your code in R)and answers. Conduct the hypothesis
and solve questions by using R.
2) A random sample of 12 graduates of a secretarial school averaged 73.2 words per minute
with a standard deviation of 7.9 words per minute on a typing test. What can we conclude,
at the .05 level, regarding the claim that secretaries at this school average less than 75
words per minute on the typing test? (You may treat the number of words that a secretary
types in one minute as being normally distributed.)

Problem #1 -- Historically, 20% of graduates of the engineering school at a major university have been women. In a recent, randomly selected graduating class of 210 students, 58 were females. Does the sample data present convincing evidence that the proportion of female graduates from the engineering school has shifted (changed)? Use α = 0.05.

A. Explain what it means to make a Type I error and indicate the probability of it occurring, under the assumption the null hypothesis was true.

B. Explain what it means to make a Type II error and suggest a possible value of the parameter in order for such an error to occur.