A psychology professor assigns letter grades on a test according to the following scheme.

A: Top 10%of scores

B: Scores below the top 10%and above the bottom 55%

C: Scores below the top 45%and above the bottom 20%

D: Scores below the top 80%and above the bottom 7%

F: Bottom 7%of scores

Scores on the test are normally distributed with a mean of 67.6and a standard deviation of 9. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Suppose you are interested in whether the GPAs of college athletes are significantly different from the GPAs of the college athlete population. To investigate this, you obtain a random sample of academic records of 5 athletes and compare their GPA to the known student population.

Here are your data:

Using an alpha = .05, what is your alternative/research hypothesis?

The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.9 cm.

a. Find the probability that an individual distance is greater than 211.80 cm.

b. Find the probability that the mean for 20 randomly selected distances is greater than 200.70 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

1. The data below represents the amount that a sample of fifteen customers spent for lunch ($) at a fast-food restaurant:

8.42   6.29   6.83   6.50   8.34   9.51   7.10   6.80   5.90   4.89   6.50   5.52   7.90   8.30   9.60

• At the 0.01 level of significance, is there evidence that the mean amount spent for lunch is different from $6.50? Follow and show the 7 steps for hypothesis testing.  
• Determine the p-value and interpret its meaning.
• What assumption must you make about the population distribution in order to conduct the test in part a? Is the assumption valid? Use and include an appropriate graph from Minitab. Write a couple of sentences supporting your answer.  
• Verify your results using Minitab by attaching or including the Minitab output.

2. Of 900 surveyed active LinkedIn members, 368 reported that they are planning to spend at least $1,000 on consumer electronics in the coming year.

• At the 0.05 level of significance, is there evidence that the percentage of all LinkedIn members who plan to spend at least $1,000 on consumer electronics is greater than 38%? Follow and show the 7 steps for hypothesis testing.
• Determine the p-value and interpret its meaning.
• What assumption must you make in order to conduct the test in part a? Demonstrate if the assumption is met.  
• Verify your results for parts a and b using Minitab. Attach or include your output.  

A researcher examined whether the time of day someone exercises affects memory retention in college courses.  Participants were assigned to one of three exercise groups: morning, afternoon, evening, and their performance on a memorization task was measured.  This data is below:

Assuming the researcher wants to know whether the performance was different in these groups (alpha = .05).  What is the Mean Squares Within (SS_W)?  Round to two decimal places.

Suppose you were attending a university where students hated the bookstore and their aggressively high prices. Suppose further that a student organization goes to the bookstore and argues that prices of text books are exceeding $150 per class. At such outrageous prices, students can no longer afford to go to school. The college bookstore claims that an average student pays $101.75 per class for texts (far below the stated claim of $150). A student group randomly selects ten courses from the catalog and finds the costs for each: $140, $125, $150, $124, $143, $170, $125, $94, $127, and $53.

a. Is that enough to justify a claim that the bookstore is underestimating the amount spent? Make sure that you show your work.

b. Students decide to take a sample from one more class and find that this class has a textbook cost of $195. Does adding this observation to the other 10 observations change your answer to part (a) above?

what is Straw man and what type of error is this

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 66.8 grams and a standard deviation of 1.94 grams.

a) For samples of size 16 pizza slices, what is the standard deviation for the sampling distribution of the sample mean?

b) What is the probability of finding a random slice of pizza with a mass of less than 66.3 grams?

c) What is the probability of finding a 16 random slices of pizza with a mean mass of less than 66.3 grams?

d) What sample mean (for a sample of size 16) would represent the bottom 15% (the 15th percentile)?  grams

A researcher examined whether the time of day someone exercises affects memory retention in college courses.  Participants were assigned to one of three exercise groups: morning, afternoon, evening, and their performance on a memorization task was measured.  This data is below:

Assuming the researcher wants to know whether the performance was different in these groups (alpha = .05).  What is the Sum of Squares Between (SS_B)?  Round to two decimal places.

2 The Civil War. A national survey conducted among a simple random sample of 1,507 adults shows that 56% of Americans think the Civil War is still relevant to American politics and political life.

(a) Conduct a hypothesis test to determine if these data provide strong evidence that the majority of the Americans think the Civil War is still relevant.

(b) Interpret the p-value in this context.

(c) Calculate a 90% confidence interval for the proportion of Americans who think the Civil War is still relevant. Interpret the interval in this context, and comment on whether or not the confidence interval agrees with the conclusion of the hypothesis test

In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product, 240 of these people said they never did so. Reasons cited for their behavior included too many steps in the process, amount too small, missed deadline, fear of being placed on a mailing list, lost receipt, and doubts about receiving the money.

Calculate an upper confidence bound at the 95% confidence level for the true proportion of such consumers who never apply for a rebate. (Round your answer to four decimal places.)

8) Scores on an exam have a normal distribution with a mean of 80 and a standard deviation of 12.

a) Find the probability that a person would score above 90.

b) Find the probability that a person would score between 75 and 85.

c) Find the probability that a group of 7 people would have a mean score above 84.

d) Find the score needed to be in the top 10% of the class.

For each combination of sample size and sample proportion, find the approximate margin of error for the 95% confidence level. (Round the answers to three decimal places.) (a) n = 200, p̂ = 0.53. (b) n = 500, p̂ = 0.53. (c) n = 500, p̂ = 0.30. (d) n = 500, p̂ = 0.60. (e) n = 800, p̂ = 0.50.

Suppose that in a random sample of 450 employed Americans, there are 57 individuals who say that they would fire their boss if they could. Calculate a 90% confidence interval for the population proportion who would fire their boss if they could. (Round the answers to three decimal places.) to

In a randomly selected sample of 400 registered voters in a community, 140 individuals say that they plan to vote for Candidate Y in the upcoming election. (a) Find the sample proportion planning to vote for Candidate Y. (Round your answer to two decimal places.) (b) Calculate the standard error of the sample proportion. (Round your answer to three decimal places.) (c) Find a 95% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y. (Round your answers to three decimal places.) to (d) Find a 98% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y. (Round your answers to three decimal places.) to