Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p1 be the proportion of customer complaints with the old dough and p2 be the proportion of customer complains with the new dough. Based on a 95% confidence for the difference of the proportions, what can be concluded? Multiple Choice

A. Reject H0, we can conclude the proportion of customer complaints is more for the old dough

B.Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

C. Do not reject H0, we can conclude the proportion of customer complaints is more for the old dough

D. Reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

Show how to compute the conditional probability of a straight flush given that the first two cards you are dealt are the 9 and 10 of hearts.

Research risk-neutral and real-world probabilities and give an example of each. In your opinion should researchers use real-world or risk-neutral default probabilities for calculating credit value at risk and adjusting the price of a derivative for defaults? Why? How would real-world probabilities affect the credit value? Explain.

An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 39.1, and 51.48. Calculate the sample mean and sample standard deviation. Round your answers to 2 decimal places.

Sample mean =

Sample standard deviation =

On the morning of March 5, 1996, a train with 14 tankers of propane derailed near the center of the small Wisconsin town of Weyauwega. Six of the tankers were ruptured and burning when the 1700 residents were ordered to evacuate the town. Researchers study disasters like this so that effective relief efforts can be designed for future disasters. About half of the households with pets did not evacuate all of their pets. A study conducted after the derailment focused on problems associated with retrieval of the pets after the evacuation and characteristics of the pet owners. One of the scales measured "commitment to adult animals," and the people who evacuated all or some of their pets were compared with those who did not evacuate any of their pets. Higher scores indicate that the pet owner is more likely to take actions that benefit the pet. Here are the data summaries.

Analyze the data and prepare a short report describing the results. (Use α = 0.01. Round your value for t to three decimal places and your P-value to four decimal places.)

State your conclusion.

Reject the null hypothesis. There is not significant evidence of a higher mean score for people who evacuated all or some pets.

Fail to reject the null hypothesis. There is significant evidence of a higher mean score for people who evacuated all or some pets.     

Fail to reject the null hypothesis. There is not significant evidence of a higher mean score for people who evacuated all or some pets.

Reject the null hypothesis. There is significant evidence of a higher mean score for people who evacuated all or some pets.

The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For the data from the first 11​ cars, the​ least-squares regression line is y=−0.0062x+42.4755. A twelfth car weighs 2,705 pounds and gets 14 miles per gallon. Compute the coefficient of determination of the expanded data set​ (including the twelfth​ car). What effect does the addition of the twelfth car to the data set have on Rsquared2​?

Car   Weight_(pounds)_x   Miles_per_Gallon_y
1   3765   21
2   3980   19
3   3532   22
4   3174   21
5   2582   27
6   3729   18
7   2601   26
8   3775   18
9   3313   19
10   2991   26
11   2753   26
12   2705   14

1) The coefficient of determination of the expanded data set is

2)How does the addition of the twelfth car to the data set affect Rsquared2​? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

a) It increases by __

b) It decreases by __

c) it does not affect it

The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table provided below ("SOCR data 2008," 2013). Countries that are considered high-income have a mean economic dynamism of 60.29. Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Test at the 5% level. Economic Dynamism of Middle Income Countries

25.8057 37.4511 51.915 43.6952 47.8506 43.7178 58.0767 41.1648 38.0793 37.7251 39.6553 42.0265 48.6159 43.8555 49.1361 61.9281 41.9543 44.9346 46.0521 48.3652 43.6252 50.9866 59.1724 39.6282 33.6074 21.6643

a) What is the appropriate test for this case? (10 points)

b) What is the null hypothesis? (5 points)

c) What is the alternative hypothesis? (5 points)

d) Determine if this test is left-tailed, right-tailed, or two-tailed. (5 points)

e) What is the significance level? (5 points)

f) What is the test statistic? (10 points) g) What is the p-value? (10 points)

h) Do we reject the null hypothesis? (5 points)

i) What is the conclusion? (15 points)

j) What is 95% confidence interval for the population mean? (10 points)

k) Interpret the confidence interval. (15 points)

According to the South Dakota Department of Health, the number of hours of TV viewing per week is higher among adult women than adult men. A recent study showed women spent an average of 33 hours per week watching TV, and men, 24 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 5.0 hours and is 5.9 hours for the men.

What percent of the women watch TV less than 36 hours per week? (Round your z-score computation and final answer to 2 decimal places.)

What percent of the men watch TV more than 20 hours per week? (Round your z-score computation and final answer to 2 decimal places.)

How many hours of TV do the four percent of women who watch the most TV per week watch? Find the comparable value for the men. (Round your answers to 3 decimal places.)

A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the infants in another group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age.

(a)

Is there significant evidence that the mean hemoglobin level is higher among breast-fed babies? State H₀ and H_a.

H₀: μ_breast-fed > μ_formula;   H_a: μ_breast-fed = μ_formulaH₀: μ_breast-fed < μ_formula;   H_a: μ_breast-fed = μ_formula     H₀: μ_breast-fed ≠ μ_formula;   H_a: μ_breast-fed < μ_formulaH₀: μ_breast-fed = μ_formula;   H_a: μ_breast-fed > μ_formula

Carry out a t test. Give the P-value. (Use α = 0.01. Use μ_breast-fed − μ_formula. Round your value for t to three decimal places, and round your P-value to four decimal places.)

What is your conclusion?

Fail to reject the null hypothesis. There is significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Reject the null hypothesis. There is significant evidence that the mean hemoglobin level is higher among breast-fed babies.     

Fail to reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

(b)

Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants. (Round your answers to three decimal places.)

(c)

State the assumptions that your procedures in (a) and (b) require in order to be valid.

We need sample sizes greater than 40.

We need two independent SRSs from normal populations.     

We need two dependent SRSs from normal populations.

We need the data to be from a skewed distribution.

Mindset Quiz

Mindset is the way that we approach learning and finding solutions. With a fixed mindset, people assume that there’s a “best way” to find a solution, and that they a specific amount of ability to learn. With a growth mindset, you realize that there are many good ways to find solutions, and that you can always learn more and become better. A higher score on the mindset quiz means that the student has more of a growth mindset. In these examples, the units are points.

A higher score on the mindset quiz means that the student has more of a growth mindset.  In these examples, the units are points.

6. Compute the mean of the mindset quiz scores for the Post-test.

Show your numerator and denominator.  

7. What is the mode of the Post-test mindset quiz scores?

8. What is the median of the Post-test mindset quiz scores?

9. Based on the mean, median, and mode, do you think the Post-test distribution is positively skewed, negatively skewed, or not skewed?

10. Knowing that a higher score on the mindset quiz means that the student has more of a growth mindset, and knowing the mean, median, and mode and what the distribution looks like, what do you think about the group of students who took the Post-test?

1. Your boastful roommate claims that fans for the Chicago Bears (the city’s football team) are simply more intelligent than the average person. With your newly-developed statistical tools, you decide to put this hypothesis to the test. You know that the standard intelligence quotient (IQ) score has a population mean of 100 with a standard deviation of 15. You find that a random sample of 121 Bears fans has an average IQ score of 103. Use this evidence to test your roommate’s argument that Bears fans are more intelligent than the general population.

1. (1 point) In symbols or words, what is the null hypothesis for this test? _____________

2. (1 point) In symbols or words, what is the alternative hypothesis for this test? _______

3. (1 point) Is this a one-sided or two-sided test? How do you know? _________________

4. (1 point) Will you use a z-test or a t-test in this situation? Why? ___________________

5. (1 point) What is the critical value of the test statistic given an α level of 0.05? ______

6. (2 points) What is the value of the test statistic calculated from the sample results?

7. (2 points) What is your decision about the null hypothesis, and what does this indicate about the intelligence of Bears fans relative to the average person?________________

8. (3 points) Would your decision be different if you used an alpha level of .01? Explain.   

The failure time T (in hours of use) for a particular electronics component follows an exponential distribution with parameter λ. Find the probability that a failure time is somewhere within 1 standard deviation of the mean failure time. Explain in words what you did to solve this, and then tell me your final answer.

Assume that a simple random sample has been selected and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. Listed below are brain volumes in cm3 of unrelated subjects used in a study. Use a 0.01 significance level to test the claim that the population of brain volumes has a mean equal to 1100.6 cm3.

1. What are the​ hypotheses?

2. Identify the test statistic t=______

3. Identify the P-value p=____

4. State the final conclusion that addresses the original claim.

A simple random sample of 100 flights of a large airline (call this airline 1) showed that 64 were on time. A simple random sample of 100 flights of another large airline (call this airline 2) showed that 80 were on time. Let p1 and p2 be the proportion of all flights that are on time for these two airlines.

21.Suppose we wish to conduct the test at a 10% significance level. What would our decision be? Based on that decision, what type of mistake could we have made?A)Do not reject H0, Type I errorB)Do not reject H0, Type II errorC)Reject H0, Type I errorD)Reject H0, Type II error

The carapace lengths (in mm) of crayfish were recorded for samples from two sections of a stream

in Kansas.

section1 5, 11, 16, 8, 12

section2 17, 14,15, 21,19, 13

1. Use the data in problem 4 for the following:

a. For the Wilcoxon Rank-Sum Test Statistic, W, compute E(W) and Var(W).

b. Compute the Z-score for the normal approximation for the data provided in the text.

c. Give the approximate p-value for a two-sided test (you do not need to show all steps of the test) and compare with the two-sided exact p-value of 0.030.

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