A survey in the N.Y. Times Almanac finds the mean commute time (one way) is 25.4 minutes for the 15 largest US cities. The chamber of commerce in a city feels that their commute time is less and wants to publicize this fact. The mean for 25 randomly selected commuters is 21.1 minutes with a standard deviation of 5.3 minutes. At the α = 0.10 level, is the city's commute significantly less than the mean commute time for the 15 largest US cities? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) A.) State the p-value. (Round your answer to four decimal places.) B.) State alpha. (Enter an exact number as an integer, fraction, or decimal.)

A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 19 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 62 minutes, with standard deviation 15 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.

Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4538 patients treated with the​ drug,145 developed the adverse reaction of nausea. Construct a 99% confidence interval for the proportion of adverse reactions.

A.) find the best point of the estimate of the population of portion p.

B.) Identify the value of the margin of error E.

C.) Construct the confidence interval. Round to 3 decimal places

D.) Write a statement that correctly interprets the confidence interval.

A patient named Diana was diagnosed with Fibromyalgia, a long-term syndrome of body pain, and was prescribed anti-depressants. Being the skeptic that she is, Diana didn't initially believe that antidepressants would help her symptoms. However after a couple months of being on the medication she concludes that the antidepressants are working, because she feels that her symptoms are in fact getting better.

Assume that among households with an annual income over $100,000, 75% own SUVs, while among households with an annual income under $100,000, only 25% do. Households making over $100,000 make up one quarter of all households in the country.

What are the odds that an SUV driver's household income is over $100,000? Choose the best answer.

A) 3/16

B) 15/31

C) 1/2

D) 9/16

A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:

Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.

H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅
H_a: at least two μ_i's are equalH₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅
H_a: all five μ_i's are equal    H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
H_a: all five μ_i's are unequalH₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
H_a: at least two μ_i's are unequal

Test the relevant hypotheses using analysis of variance with α = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)

Give the test statistic. (Round your answer to two decimal places.)
f =

What can be said about the P-value for the test?

P-value > 0.1000.050 < P-value < 0.100    0.010 < P-value < 0.0500.001 < P-value < 0.010P-value < 0.001

State the conclusion in the problem context.

Fail to reject H₀. There are no differences in the true average axial stiffness for the different plate lengths.Reject H₀. There are differences in the true average axial stiffness for the different plate lengths.    Reject H₀. There are no differences in the true average axial stiffness for the different plate lengths.Fail to reject H₀. There are differences in the true average axial stiffness for the different plate lengths.

oyota USA is studying the effect of regular versus high-octane gasoline on the fuel economy of its new high-performance, 3.5-liter, V6 engine. Ten executives are selected and asked to maintain records on the number of miles traveled per gallon of gas. The results are:

a. STATE THE NULL HYPOTHESIS AND ALTERNATE HYPOTHESIS

Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of patients with SAD to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)

(b) Compute Tukey's HSD to analyze the significant main effect.

The critical value is ____ for each pairwise comparison.

(c) Summarize the results for this test using APA format.

The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the regular and reduced prices at the randomly selected outlets.

At the 0.050 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Hint: For the calculations, assume reduced price as the first sample.

1. Compute the pooled estimate of the variance.

2. Compute the test statistic.

3. State your decision about the null hypothesis.

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 217 accurate orders and 58 that were not accurate. a. Construct a 95​% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part​ (a) to this 95​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.195<p< 0.281. What do you​ conclude?

A large university is interested in the outcome of a course standardization process. They have taken a random sample of 100 student grades, across all instructors. The grades represent the proportion of problems answered correctly on a midterm exam. The sample proportion correct was calculated as 0.78.

a. Construct a 90% confidence interval on the population proportion of correctly answered problems.

b. Construct a 95% confidence interval on the population proportion of correctly answered problems.

III. A health-food store stocks two different brands of certain type of grain. Let X = the amount (lb) of brand A on hand and Y = the amount of brand B on hand. Suppose the joint pdf of X and Y is

?k(x+2y) ifx≥0,y≥0,x+y≤10

f(x,y) =
Keep four decimals if necessary.

(8 pts) a. Draw the region of positive density and determine the value of k. (8 pts) b. Are X and Y independent? Answer by first deriving the

marginal pdf of each variable.
(8 pts) c. Compute P (X + Y ≤ 5). (8 pts) d. Compute E(XY ).
(8 pts) e. Compute Cov(X, Y ).

We operate a bottle filling factory. One of our machines fills a 32-ounce bottle with a target of 32.08 ounces of orange juice. Every 10 minutes or so we obtain a sample filled bottle and hold it for the quality control department who will weigh the approximately 50 such bottles to determine if the machine is performing correctly. If the average of the 50 bottles is less than 32 ounces, the machine is shut down and the entire production from that 8-hour shift is held until further tests are performed.

1. We know that over the years this machine delivers 32.082 ounce of orange juice with a standard deviation 0.01 ounces. What is the probability that a sample of 50 bottles has a mean volume of less than 32 ounces?

1. There are 1,008 8-hour shifts per year (allowing for holidays, maintenance and a two-week scheduled shutdown). In a typical year, hour many times do we expect the quality department to shut down the machine and hold that shift’s production?

female sample size: 62

male sample size: 30

9. Let’s look a little closer at the original dataset (both genders, without Audrey/Katrina added) and actually perform a hypothesis test. At α = 0.05​, can you support the claim that female hurricanes are more deadly than male hurricanes?

9a. (4 pts) Write out the hypotheses statements below and identify the parameter(s) of interest.

Ho: _____________________ Parameters of interest: _______________________________________

Ha: _____________________ _______________________________________

9b. (1 pt) Which hypothesis represents the claim? Circle one: Null Hypothesis (H0) or Alternative Hypothesis (Ha)

assume that you would like to compare the mean number of hospital visits per person per year between Texas and California.  Specifically you would like to test if Texans have a different mean number of visitations per year per person than Californians.  In order to do this, you take a random sample of 29 Texans and 24 Californians and ask each of them how many times they visited the Emergency room last year.  The average number of visits for the Texans was 1.158 with a sample standard deviation of .022 while the average number of visits for Californians was 1.378 with a sample standard deviation of .035.  You may assume the distribution of visits in both Texas and California are normally distributed with the same standard deviation.  Assume alpha is 0.01.  

1. What is(are) the critical value(s) for this study?
   1. ± 1.674         b. ±2.40         c. 2.40      d. ±1.675   e.  1.675      f. ± 2.672       g.  ± 2.676          h. 2.676    i.   – 1.674

2. Perform the appropriate test and select the proper conclusion.
   1. There is overwhelming evidence (pvalue < .0001) that the mean number of Emergency Room visits in Texas and California are different.  
   2. There is not sufficient evidence to suggest (pvalue = 1.566) that the mean number of Emergency Room visits in Texas and California are different.  
   3. There is overwhelming evidence (pvalue < .0001) that the proportion of Emergency Room visits in Texas and California are different.
   4. There is not sufficient evidence (pvalue = 1.566) that the proportion of Emergency Room visits in Texas and California are different.
   5. There is not sufficient evidence (pvalue < .0001) that the mean number of Emergency Room visits in Texas and California are different.

3. T  /  F  A 90% confidence interval for the true proportion p is wider than a 95% confidence interval when calculated on the same data set.  

4. T  /  F  If we get a P-value of 0.56, this means we have proven the null hypothesis to be true.