A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university’s belief, how does one define the population parameter of interest?

Multiple Choice

• It’s the proportion of honors graduates with a GPA of 3.00 or below.

• It’s the standard deviation of the number of honors graduates with a GPA of 3.00 or below.

• It’s the number of honors graduates with a GPA of 3.00 or below.

• It’s the mean number of honors graduates with a GPA of 3.00 or below.

5. Suppose that researchers study a sample of 50 people and nd that 10 are left-handed.

(a) Find a 95% confidence interval for the population proportion that is left-handed.

(b) What would the confidence interval be if the researchers used the Wilson value ~p instead?

(c) Suppose that an investigator tests the null hypothesis that the population proportion is 18% against the alternative that it is less than that. If = 0:05 then nd the critical value ^pc. Using ^p as the sample estimate, would the investigator reject the null?

(d) Suppose that researchers are using this critical value but, unbeknownst to them, the true, population proportion is 0.16. Find the power of the test.

Use R to solve the following problem: A study was carried out to investigate the variation of rainbow trout weights in a certain creek. The weights (in kilograms) of 10 randomly selected fish are listed below: 0.78, 0.45, 0.35, 0.76, 0.57, 0.42, 0.33, 0.68, 0.66, 0.42

Assume that the population is approximately normally distributed. Test the hypothesis that the unknown population variance is less than 0.08 kg2 at alpha=0.05. Be sure to list (i) your hypotheses, (ii) test statistic, (iii) decision, and (iv) conclusion.

A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 33 that have no defects. What is the probability that at least one of the calculators is​ defective?

(1) Consider the random experiment where three 6-sided dice are rolled and the number that comes up (1, 2, 3, 4, 5 or 6) on each die is observed.

(a) What is the size of the sample space S of this random experiment?

(b) Find the probability of event E1: “All three numbers rolled are the same.”

(c) Find the probability of event E2: “The sum of the three numbers rolled is 5.”

(d) Find the probability of event E3: “At least one 6 is rolled.” (Hint: it may help to first find the probability of the complementary event.)

Assume that systolic blood pressure (SBP) in a population is normally distributed with a mean of 120 mmHg and a standard deviation of 10 mmHg

- What percent of the population has an SBP > 130 mmHg?

- What percent of the population has an SBP in the range of 110 to 140 mmHg inclusive?

- What percent of the population has an SBP > 150 or < 110 mmHg?

Fill in blanks of the following statements.

Bottom 10% of this population would have SBP of less than _______ mmHg

Top 5 % of this population would have SBP of at least _______ mmHg

10. State which is the most appropriate: z or t or neither. Give the critical value when you can.

            95% confidence; ; ; population has an outlier

11. We want to know if the percentage of last-born children who are the most assertive has changed from the 43% estimate from a study in 2017. How many families should be selected to produce an estimate that is within 1.2% of the population percentage with 98% confidence?

Based on past data, the sample mean of the credit card purchases at a large department store is $45. Assuming sample size is 25 and the sample standard deviation is 9.

a)          What % of samples are likely to have between 25 and 35?                                                                  ___________

b)         Between what two values 95% of sample means fall?                                                                         ___________

c)          Below what value 98% of sample means fall?                                                                                   ___________

d)         Above what value only5% of sample means fall??                                                                             ___________

Within what symmetrical limits of the population percentage will 95% of the sample percentages fall?

2. In a random sample of 857 families with multiple children, it was found that 533 of them prefer Charmin brand toilet paper. Test the claim that the proportion is larger than 0.61 using a 0.05 significance level.

a. Give the critical region and the value of the test statistic.

b. Give the decision and conclusion.

5.35 Gaming and distracted eating, Part I: A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decrease in the amount of food consumption. To test this hypothesis, they monitored food intake for a group of 44 patients who were randomized into two equal groups. The treatment group ate lunch while playing solitaire, and the control group ate lunch without any added distractions. Patients in the treatment group ate 52.1 grams of biscuits, with a standard deviation of 45.1 grams, and patients in the control group ate 27.1 grams of biscuits, with a standard deviation of 26.4 grams. Do these data provide convincing evidence that the average food intake (measured in amount of biscuits consumed) is different for the patients in the treatment group? Assume that conditions for inference are satisfied.


What are the hypotheses for this test?

• Ho: μ_{no distraction} = μ_distraction
  Ha: μ_{no distraction} > μ_distraction
• Ho: μ_{no distraction} = μ_distraction
  Ha: μ_{no distraction} < μ_distraction
• Ho: μ_{no distraction} = μ_distraction
  Ha: μ_{no distraction} ≠ μ_distraction

The test statistic for the hypothesis test is:  (please round to two decimal places)
The p-value for the hypothesis test is:  (please round to four decimal places)
Interpret the result of the hypothesis test in the context of the study:

• Since p < α we do not have enough evidence to reject the idea that the average biscuit consumption in the two groups was the same
• Since p < α we have enough evidence to accept the idea that the average biscuit consumption in the two groups was the same
• Since p < α we have enough evidence to reject the idea that the average biscuit consumption in the two groups was the same, and accept the alternative that distracted eaters will eat a different amount than non-distracted eaters, on average
• Since p < α we have enough evidence to reject the idea that the average biscuit consumption in the two groups was the same, and accept the alternative that distracted eaters will eat more than non-distracted eaters, on average

In addtion to the questions, make sure to display the regions under the normal distribution curve.

The monthly income of residents of Big City is normally distributed with a mean of $3000 and a standard deviation of $500.

a. The mayor of Big City makes $2,250 a month. What percentage of Big City's residents has incomes that are more than the mayor's?

b. Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes?

c. What are the minimum and the maximum incomes of the middle 95% of the residents?

d. Two hundred residents have incomes of at least $4,440 per month. What is the population of Big City?

Chapter P, Section 1, Exercise 037

During the 2015-16 NBA season, Jodie Meeks of the Detroit Pistons had a free throw shooting percentage of 0.906 . Assume that the probability Jodie Meeks makes any given free throw is fixed at 0.906 , and that free throws are independent. Let S denote Successfully making a free throw and F denotes missing it.

( Round ALL your answers to four decimal places. )

(a) If Jodie Meeks shoots TWO free throws in a game, what is the probability that he makes BOTH of them?

P(Makes two) ______

(b) If Jodie Meeks shoots TWO free throws, what is the probability that he misses both of them?

P(Misses two) ____________

(c) If Jodie Meeks shoots TWO free throws, what is the probability that he makes exactly one of them?

P(Makes exactly one) ________________

Suppose an audit process is taking place at a small airport, and the head
auditor arrives randomly throughout the day and assesses the operation of the airport.
She shows up in one-hr intervals at a time. The time between aircraft arrivals at this
small airport is exponentially distributed with a mean of 75 minutes. You may assume
the operation of the small airport is independent of the time interval under consideration.
a) What is the probability that at least four aircrafts arrive within an hour?
b)What is the probability that more than three and less than six aircrafts arrive within an
hour?
C)What is the amount of time (in hours) such that the probability of aircraft arrivals in the
interval is 75%?
D) What is the probability that the third interval the auditor shows up for is the second
interval with at least four aircraft arrivals?
e) If the auditor decides to show up four different times in a day, what is the mean of the
number of intervals she will experience with less than four aircraft arrivals?

What are some of the similarities between Expectation Maximization and K-mean aside form both being clustering methods.

Based on an online survey done recently, the company asked a variety of questions regarding internet and email practices of a randomly selected sample size of 750 people aged 18 to 25 and 250 people that are over 65 years of age. In response to the question about whether the person has ever clicked on a link in an unsolicited email to get more information, 32% of the young people and 25% of the older folks said yes. Are these two groups equally likely to clinic on a link in an unsolicited email? In other words, does one group practice ‘safe clicking’ more than the other? Use a 95% confidence level. Report a p-value. Is this a weak or strong conclusion? 2 pts.