A baseball player has a lifetime batting average of 0.168. If, in a season, this player has 460 "at bats", what is the probability he gets 101 or more hits?

Probability of 101 or more hits =

Answer is not .0015 or .0019.

The pH of a liquid is a measure of its acidity or alkalinity. Pure water was a pH of 7, which is neutral. Solutions with a pH less than 7 are acidic while solutions with a pH greater than 7 are alkaline. A biologist was interested in testing the purity of lake water in Florida. A random sample of 59 lakes was taken, and the pH of water in each lake was recorded. The sample of lakes had an average pH of 6.729 with a standard deviation of 1.827.   

Using a significance level of 0.10, is there evidence the mean pH of Florida lakes is not neutral?

• What hypotheses should be tested?

  Ho:μ=7Ho:μ=7
  Ha:μ<7Ha:μ<7

  Ho:μ≠7Ho:μ≠7
  Ha:μ=7Ha:μ=7

  Ho:μ=7Ho:μ=7
  Ha:μ>7Ha:μ>7

  Ho:μ=7Ho:μ=7
  Ha:μ≠7Ha:μ≠7

• αα =  
• Test Statistic: t =   (Note: round the t-score to two decimal places)
• probability = Select an answer 0.8704 0.1296 0.2592   
• decision: Select an answer Reject H₀ Fail to reject H₀
• At the 0.10 level, there Select an answer is not is   significant evidence to conclude the mean pH in Florida lakes is Select an answer different than greater than less than  7.

Based on the decision of your test and the sample selected, what can you conclude?

• The mean pH of Florida lakes is neutral.
• The mean pH of Florida lakes is acidic.
• The mean pH of Florida lakes is alkaline.

According to U.S. News & World Report's publication America's Best Colleges, the average cost to attend the University of Southern California (USC) after deducting grants based on need is $26,950. Assume the population standard deviation is $7,800. Suppose that a random sample of 70 USC students will be taken from this population. Use z-table.

a. What is the value of the standard error of the mean?

(to nearest whole number)

b. What is the probability that the sample mean will be more than $26,950?

(to 2 decimals)

c. What is the probability that the sample mean will be within $750 of the population mean?

(to 4 decimals)

d. How would the probability in part (c) change if the sample size were increased to 160 ?

(to 4 decimals)

1. The annual earnings of 25 people with a high school diploma and 16 people with an associate degree are shown below. Can you conclude that there is a difference in the mean annual earnings based on level of education? Assume that population are normally distributed and population variances are not equal.

1. Identify the claim and state the null and alternative hypothesis.

2. What type of statistical test should be used to answer the researcher’s question?

(Note: Is this a z-test or a t-test? One sample, dependent sample or independent sample)

3. Find the standardized test statistic and corresponding critical value(s).

4. At 0.05 significance level, decide whether to reject or fail to reject the null hypothesis.
5. Interpret the decision in the context of the original claim.

Question 1

Researchers are interested in testing the effectiveness of a new immunosuppressive therapy to be used post-transplant to reduce graft failure in the host. Suppose researchers investigating this new therapy are concerned about the dangerous side-effects of the drug. For instance, participants that would like to enroll in the study are not allowed to already have diabetes, as the immunosuppressive agent has been found to drastically increase fasting glucose levels, which could be very dangerous for diabetics. This means, however, that participants that enter and are treated with the new drug may develop diabetes as time goes on. Suppose the following table addresses the incidence of diabetes in the study depending on treatment group.

A) Calculate the incidence of diabetes in the group after the follow-up period.

B) Calculate the relative risk of diabetes due to the investigational drug in the study.

C) Carry out a formal chi-square test to determine if there is a significant difference in diabetes between the two groups. Write out your null and alternative hypotheses at the 0.05 alpha level.

Choose the most appropriate option

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 490 viewers. After viewing the comedy, 420 indicated they would watch the new show and suggested it replace the crime investigation show.   

a. Estimate the value of the population proportion. (Round the final answer to 3 decimal places.)

Estimate of proportion           

b. Compute the standard error of the proportion. (Round the final answer to 3 decimal places.)

Standard error of the proportion             

c. Develop a 95% confidence interval for the population proportion. (Round the final answers to 3 decimal places.)

The confidence interval is between  and  .

d. Interpret your findings. (Round the final answers to the nearest whole number.)

We are reasonably sure the population proportion is between  and  %.

1. For the network below:
   1. Calculate T-E and Variance for each activity. Assume the durations have 95% certainty (i.e. the range from optimistic to pessimistic durations covers 95% of all possible durations).
   2. Calculate the expected duration of the network. Do not use Crystal Ball.
   3. What is the probability the network will take no more than 23 days?   Use the Z-table or Excel’s NORM.DIST formula, not Crystal Ball. Be sure to show all work.

The question to address is: “What have you learned about statistics?” In developing your responses, consider—at a minimum—and discuss the application of each of the course elements in analyzing and making decisions about data (counts and/or measurements).

• Descriptive statistics
• Inferential statistics

Consider the following data for the patients taking the drug (Ascorbic Acid).

What is the probability that a patient has No Cold? Is this a marginal or joint probability?

a) 0.18 marginal

b) 0.62 marginal

c) 0.82 marginal

d) 0.82 joint

e) 0.86 joint

Question 15

What is the probability that a patient is taking Placebo and has No Cold? Is this a marginal or joint probability?

a) 0.86 joint

b) 0.33 joint

c) 0.33 marginal

d) 0.82 marginal

e) 0.82 joint

Question 16

What is the probability that a patient is taking Placebo or has No Cold and identify the correct formula for this kind of probability?

a) 0.92 F5c

b) 0.87 F5a

c) 0.33 F5c

d) 0.92 F5b

e) 0.87 F5b

Question 17

Find conditional probability P(No Cold | taking the drug), P(No Cold | taking Placebo), P(taking drug | No Cold) and identify the correct formula for this kind of probability?

a) 0.49, 0.33, 0.82 F5ef

b) 0.18, 0.62, 0.82 F5c

c) 0.6, 0.71, 0.79, F5ef

d) 0.79, 0.86, 0.6 F5g

e) 0.79, 0.86, 0.6 F5ef

Question 18

Based on answers to previous questions the row and column variables are ________ (a) independent (b) dependent (c) marginal (d) conditional (e) joint

a) marginal

b) joint

c) dependent

d) independent

e) conditional

A recent study of two vendors of desktop personal computers reported that out of 895 units sold by Brand A, 118 required repair, while out of 711 units sold by Brand B, 98 required repair. Round all numeric answers to 4 decimal places.

1. Calculate the difference in the sample proportion for the two brands of computers, ?̂ ??????−?̂ ??????p^BrandA−p^BrandB =  .

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of computers needing repairs is different for the two brands.

A. ?0:??−??=0H0:pA−pB=0, ??:??−??<0HA:pA−pB<0
B. ?0:??−??=0H0:pA−pB=0, ??:??−??≠0HA:pA−pB≠0
C. ?0:??−??=0H0:pA−pB=0, ??:??−??>0HA:pA−pB>0

3. Calculate the pooled estimate of the sample proportion, ?̂ p^ =

4. Is the success-failure condition met for this scenario?

A. Yes
B. No

5. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

6. Calculate the p-value for this hypothesis test, p-value =  .

7. Based on the p-value, we have:
A. little evidence
B. strong evidence
C. some evidence
D. very strong evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.

8. Compute a 99 % confidence interval for the difference ?̂ ??????−?̂ ??????p^BrandA−p^BrandB = (  ,  )

Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.3 9.3 10.2 8.0 8.3 8.7 y 9.9 18.1 20.6 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.8, Σy = 83.3, Σx2 = 468, Σy2 = 1255.59, Σxy = 750.81, and r ≈ 0.974. (a) Draw a scatter diagram displaying the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 123456789101112345678910111213141516171819202122 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = y hat = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained % unexplained % (f) Suppose a small city in Oregon has a per capita income of 9.2 thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.) M.D.s per 10,000 residents

Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 34% of all fatal accidents of 17-year-olds are due to speeding. x 17 27 37 47 57 67 77 y 34 22 22 12 10 7 5 Complete parts (a) through (e), given Σx = 329, Σy = 112, Σx2 = 18,263, Σy2 = 2442, Σxy = 3974, and r ≈ −0.956. (a) Draw a scatter diagram displaying the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 5101520253035404550556065707580510152025303540 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = y hat = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained % unexplained % (f) Predict the percentage of all fatal accidents due to speeding for 35-year-olds. (Round your answer to two decimal places.) % Need Help?

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 22 people reveals the mean yearly consumption to be 32 kilograms (kg) with a standard deviation of 10 kg. Assume a normal population.

a-1. What is the value of the population mean?

Population mean            (Click to select)  Unknown  32  42

a-2. What is the best estimate of this value?

Estimate value           

b-1. Explain why we need to use the t distribution.

(Click to select)  Use the t distribution as the population standard deviation is known.  Use the t distribution as the population standard deviation is unknown.  Use the t distribution as the population mean is known.

b-2. What assumption do you need to make?

(Click to select)  We must assume that the population is normally distributed.  We must assume that the population is binomially distributed.  We must assume that the population is not normally distributed.

c. For a 90% confidence interval, what is the value of t? (Round the final answer to 3 decimal places.)

Value of t           

d. Develop the 90% confidence interval for the population mean. (Round the final answers to 3 decimal places.)

Confidence interval for the population mean is  and  .

e. Would it be reasonable to conclude that the population mean is 37 kg?

(Click to select)  No  Yes

That value is  (Click to select)  not reasonable  reasonable  because it is  (Click to select)  inside  not inside  the interval.

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.   

a. Estimate the value of the population proportion. (Round the final answer to 3 decimal places.)

Estimate of proportion           

b. Compute the standard error of the proportion. (Round the final answer to 3 decimal places.)

Standard error of the proportion             

c. Develop a 99% confidence interval for the population proportion. (Round the final answers to 3 decimal places.)

The confidence interval is between  and  .

d. Interpret your findings. (Round the final answers to the nearest whole number.)

We are reasonably sure the population proportion is between  and  %.