A teacher is interested in her students’ opinion on whether the non-required lecture is effective for them. She flips a coin every time a student walks into lecture and if it lands heads, she asks that student if they find lecture effective and records their answer.

(a) Are there any issues with creating a confidence interval with this sample if our parameter of interest is the proportion of enrolled students who find lecture effective? Explain briefly.

(b) Another lecturer asks a random sample of his students to comment on the efficacy of his lecture and fifty two (52) of the 80 students interviewed reported finding the lecture effective. Create a 98% confidence interval for the proportion of students who find his lecture effective.

Hypothesis testing conceptual questions: a. Define the null and alternative hypothesis b. What are the two errors that can occur in hypothesis testing? What mathematical symbols are used to denote these errors? c. Define the P-value. How are P-values used in hypothesis testing? d. How is the significance level of a hypothesis test determined? e. What assumptions must your data meet in order to perform a hypothesis test?

Suppose that the weights of airline passenger bags are normally distributed with a mean of 49.53 pounds and a standard deviation of 3.16 pounds.

a) What is the probability that the weight of a bag will be greater than the maximum allowable weight of 50 pounds? Give your answer to four decimal places.  

b) Let X represent the weight of a randomly selected bag. For what value of c is P(E(X) - c < X < E(X) + c)=0.96? Give your answer to four decimal places.  

c) Assume the weights of individual bags are independent. What is the expected number of bags out of a sample of 17 that weigh greater than 50 lbs? Give your answer to four decimal places.  

d) Assuming the weights of individual bags are independent, what is the probability that 8 or fewer bags weigh greater than 50 pounds in a sample of size 17? Give your answer to four decimal places.

Classified ads at a certain website offered several used cars of a certain make and model. The accompanying table lists the ages of the cars and the advertised prices. Complete parts​ a) through​ g) below.

Age (years)   Price (dollars)
1   16,000
2   14,800
3   14,800
3   14,900
3   12,900
3   13,000
4   16,200
4   12,900
4   12,300
4   10,500
4   8,000
5   14,500
5   12,300
5   11,100
5   10,000
6   11,800
6   11,000
6   10,800
6   9,800
6   8,500
7   10,200
7   9,700
7   9,000
7   7,500
7   6,000

​a) Find the equation of the regression line.

Price = _ + ( _ ) Age

​(Round to two decimal places as​ needed.)

​c) Explain the meaning of the​ y-intercept of the line. Select the correct choice below​ and, if​ necessary, fill-in the answer box to complete your choice.

​(Round to two decimal places as​ needed.)

The model predicts that the advertised price of a brand new car of this make and model is _ dollars.

d) If you want to sell a six​-year-old car of this make and​ model, what price seems​ appropriate?

_ dollars

​(Round to the nearest dollar as​ needed.)

Why is it considered risky and unreliable to use the regression formula to predict the dependent variable outside the range of the actual values of the independent variable is...

1. Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0,

22.6, 177.5, 95.4, and 220.0. Summary statistics yield x = 180.975 and s = 143.042. Calculate a 99%

confidence interval for the mean endowment of all private colleges in the United States. Note that s is sample standard deviation.

A) 180.975 ± 181.387                                                             B) 180.975 ± 169.672

C) 180.975 ± 176.955                                                             D) 180.975 ± 189.173

2) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). The researcher claimed that the average GPA of all male students exceeded 2.94. Using the confidence interval supplied above, how do you respond to this claim?

A) We are 95% confident that the researcher is correct.

B) We are 95% confident that the researcher is incorrect.

C) We are 100% confident that the researcher is incorrect.

D) We cannot make any statement regarding the average GPA of male university students at the 95% confidence level.

3) A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects

(60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). State the appropriate interpretation for this confidence interval. Note that all answers begin with "We are 95 percent confidence that…"

A) The term life insurance cost of the retired statistician's insurance policy falls between $850.00 and $1050.00

B) The average term life insurance cost for sampled 65 subjects falls between $850.00 and

$1050.00

C) The term life insurance cost for all 60-year-old male non-smokers' insurance policies falls

between $850.00 and $1050.00

D) The average term life insurance costs for all 60 -year-old male non-smokers falls between

$850.00 and $1050.00

4) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 41 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 35, s = 18. Identify the null and

alternative hypothesis for a test to determine if the mean number of tissues used during a cold is

as claimed.

A) H0: μ > 41 vs. Ha: μ ≤ 41                                                B) H0: μ = 41 vs. Ha: μ ≠ 41

C) H0: μ = 41 vs. Ha: μ < 41                                               D) H0: μ = 41 vs. Ha: μ > 41

5) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 37 minutes (no morwe). The owner has randomly selected 15 customers

and delivered pizzas to their homes. What hypotheses should the owner test to demonstrate that the pizza delivery will not be successful?

A) H0: μ = 37 vs. Ha: μ < 37                                                B) H0: μ < 37 vs. Ha: μ = 37

C) H0: μ ≤ 37 vs. Ha: μ > 37                                                D) H0: μ = 37 vs. Ha: μ ≠ 37

6) Researchers have claimed that the average number of headaches per student during a semester of Statistics is 11. In a sample of n = 16 students the mean is 12 headaches with a deviation of 2.4. Which of the following represent the null and alternative hypotheses necessary to test the students' belief?

A) H0: μ = 11 vs. Ha: μ > 11                                                B) H0: μ = 11 vs. Ha: μ < 11

C) H0: μ < 11 vs. Ha: μ = 11                                               D) H0: μ = 11 vs. Ha: μ ≠ 11

1.) An adult patient being treated for severe muscle spasms has her calcium level tested regularly because her condition could be attributed to a low calcium level. A random sample of her recent calcium levels (in mg/dL) is given below.

5.3, 6.8, 9.1, 8.9, 9.8,

5.9, 8.2, 6.1, 9.4, 9.0

(a) Find a 95% confidence interval for her mean calcium level.
(b) A person with a mean calcium level below 6 mg/dL is thought to have low calcium. Based upon your 95% confidence interval, does she have a low calcium level? Explain your reason(s).

4. The time required to prepare a dry cappuccino using whole milk at the Daily Grind Coffee

    House is uniformly distributed between 30 and 40 seconds. Assuming a customer has just

    ordered a whole-milk dry cappuccino,

1. What is the probability that the preparation time will be more than 30 seconds?
2. What is the probability that the preparation time will be within 40 seconds?
3. What is the probability that that the preparation time will be between 30 and 40 seconds?
4. What is the mean and standard deviation of preparation times for a dry cappuccino using whole milk at the Daily Grind Coffee House?

Hint: The underlined words define the population interval of preparation time.

A between-subjects factorial design has two levels of factor A and 2 levels of Factor B. Each cell of the design contains n=8 participants. The sums of squares are shown in the table. The alpha level for the experiment is 0.05. Use the provided information and partially completed table to provide the requested values.

Specifically looking for the df total and F ratio for the AxB interaction.

Big Box Store (BBS) has an annual rate of 4% of all sales being returned. In a recent sample of thirty randomly selected sales the number of returns was five.(Use binomial probability)

What is the probability that a random sample of 30 sales has less than four returns?

What is the probability that the number of returns is not equal to 4 in a random sample of 30 sales?

What is the probability that a random sample of 30 sales has more than three returns?

You may need to use the appropriate appendix table to answer this question.

According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800.

(a)

What is the probability that a household in Maryland has an annual income of $110,000 or more? (Round your answer to four decimal places.)

(b)

What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.)

(c)

What is the probability that a household in Maryland has an annual income between $60,000 and $70,000? (Round your answer to four decimal places.)

(d)

What is the annual income (in $) of a household in the eighty-sixth percentile of annual household income in Maryland? (Round your answer to the nearest cent.)

$  

For this project, you will analyze the famous casino game, Roulette. In the game of Roulette, there is a wheel consisting of 38 numbers: 18 black numbers, 18 red numbers, and 2 green numbers (0 and 00). The wheel is spun and a ball is released into the wheel. As the wheel comes to a stop, the ball will land on one of the numbers. A player will place their bet before the wheel is spun. A player can make the following bets (along with other bets):

Single (or multiple) number

1^st, 2^nd or 3^rd column (e.g. 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34)

1^st, 2^nd or 3^rd dozen (e.g. 1 through 12)

Odd / Even (does not include 0 or 00)

Red / Black

1 through 18 or 19 through 36

Please answer the following questions based on the game of Roulette:

What is the probability of betting on all odds and winning?

What is the probability of betting on the 2^nd dozen and winning?

A player bets on the number 5 in the first game; then bets on number 22 in the second game. Did the player’s odds of winning change from the first to the second game? Explain.

What is a better bet: all reds or all evens? Explain. (Hint: 0 and 00 are not included in an all even bet)

If a player always bets on 00, what is the expected winnings (or loses) when playing 20 games of Roulette given the player receives $100 if they win and owes $1 if they lose?

If a player always bets on 3 and 23, what is the expected winnings (or loses) when playing 75 games of Roulette given the player receives $120 if they win (on either number) and owes $3 if they lose?

If a player always bets on the 2^nd dozen (13 to 24), what is the expected winnings (or loses) when playing 25 games of Roulette given the player receives $32 if they win and owes $15 if they lose?

If you are playing Roulette, how would you bet? Would you play a lot of games or try to win a lot on one or two games?

A learning researcher is interested in the effectiveness of her new memory enhancement program. To test this program, she has 15 students learn a list of 50 words. Memory performance is measured using a recall test. After the first test, these same students are instructed as to how to use the memory improvement program and then learn a second list of 50 different words. Memory performance is again measured with the recall test. If you wanted to test the hypothesis to see if the memory program actually improves memory, what would be the appropriate analysis? What would be the null and alternative hypotheses for this test? Would the alternative hypothesis be one-tailed (directional) or two-tailed (nondirectional)? Why?

Consider the data.

The estimated regression equation for these data is

ŷ = 70 − 3x.

(a)

Compute SSE, SST, and SSR using equations

SSE = Σ(y_i − ŷ_i)²,

SST = Σ(y_i − y)²,

and

SSR = Σ(ŷ_i − y)².

SSE=SST=SSR=

(b)

Compute the coefficient of determination

r².

(Round your answer to three decimal places.)

r²

=

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.    The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.

(c)

Compute the sample correlation coefficient. (Round your answer to three decimal places.)

Via the same learning team as in Unit One, discuss examples of probability theory selected from your job or life (or roll dice), and share your results in a discussion post. I work at an insurance company, how can I use this within my career?