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A candy company makes chocolates in two flavors, milk and dark. Brenda is a quality control manager for the company who wants to make sure that each jumbo bag contains about the same number of chocolates, regardless of flavor. She collects two random samples of 15 bags of chocolates from each flavor and counts the number of chocolates in each bag. Assume that both flavors have a standard deviation of 9.5 chocolates per bag and that the number of chocolates per bag for both flavors is normally distributed. Let the number of milk chocolates be the first sample, and let the number of dark chocolates be the second sample.

She conducts a two-mean hypothesis test at the 0.01 level of significance, to test if there is evidence that both flavors have the same number of chips in each bag.

For this test: H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.

The test results are: z≈3.99 , p-value is approximately 0.000

Which of the following are appropriate conclusions for this hypothesis test? Select all that apply.

A. Fail to reject H0

B. Reject H0.

C. There is sufficient evidence at the 0.01 level of significance to conclude that the mean number of chocolates per bag for milk chocolates is different the mean number of chocolates per bag for dark chocolates.

D. There is insufficient evidence at the 0.01 level of significance to conclude that the mean number of chocolates per bag for milk chocolates is different than the mean number of chocolates per bag for dark chocolates.

According to the recent survey conducted by Sunny Travel Agency, a married

couple spends an average of $500 per day while on vacation. Suppose a sample of 64 couples

vacationing at the Resort XYZ resulted in a sample mean of $490 per day and a sample standard

deviation of $100. Develop a 95% confidence interval estimate of the mean amount spent per day by

a couple of couples vacationing at the Resort XYZ.

Create a case on the application of inferences about the difference between two population means (σ1 and σ2 known) and explain the hypothesis tests until conclusion.

) Grades on a standardized test are known to have a mean of 1000 for students in the US. The test is administered to 453 randomly selected students from Queens College, and they obtained an average grade of 1013 and a standard deviation of 108. a. Construct a 95 % confidence interval for the true average test score for Queens College students.(1pt) b. With 5% significance level, Is there a statistical evidence that Queens College students perform differently than other students in the US?(1pt) From now, assume the same 453 students selected earlier are now given a two-hour tutoring session and then asked to take the test a second time. The average change in their test scores is 9 points, and the standard deviation of the change is 60 points. Assume the changes are from a Normal ( , ) 2   distribution, and for every student, the change in score is the difference between the score after the tutoring session, and the score before the tutoring session c. You are asked by the school administration to study whether students have performed better in their second attempt. State in terms of  , the relevant null and alternative hypothesis in conducting this study.d. Compute the t statistic for testing ?0 against ??; obtain the p- value for the test.e. Do you reject ?0 at the 5% level? At the 1% level? f. Provide a short summary of your conclusions from this study. Comment on the practical versus statistical significance of this estimate.

The normal distribution is the preferred tool to evaluate market historical performance.

                a.            What are the basic statistics assumptions for using the normal distribution?

                b.            Under what conditions the normal distribution does not do a good job?

                c.             What statistical assumptions are not met in turbulent markets? Explain thoroughly.

                d.            Describe the most popular statistical tool for measuring portfolio risk in addition to the                 standard deviation?

The table lists height (in) and weights (lb) of randomly selected 8 students.
Height (in) 60 65 66 68 60 67 69 70

Weight (lb) 150 152 156 160 160 167 168 170

(a) Find the the value of coefficient of correlation r.
(b) Find the equation of the line of best best fit (trend line). What does variable y represents?
(c) Estimate weight of a student from the same group who is 64 inches tall.

possibility tree

One box contains two black balls (labeled B1 and B2) and one white ball. A second box contains one black ball and two white balls (labeled W1 and W2). Suppose the following experiment is performed: One of the two boxes is chosen at random. Next a ball is randomly chosen from the box. Then a second ball is chosen at random from the same box without replacing the first ball.

a. Construct the possibility tree showing all possible outcomes of this experiment.

b. What is the total number of outcomes of this experiment?

The Quinnipiac polling institute claims that 70% of college stu- dents live on campus. A researcher takes a sample of 200 college students to see if the proportion is less. In the researcher’s sample, 132 college students live on campus.

(a) Develop the null and alternative hypotheses.

(b) At α = 0.02, what is the rejection rule?

(c) What is the value of the test statistic z?

(d) Should the researcher reject H0?

(e) Based on your answer in part (d), what is our conclusion for THIS SITUATION? Be specific.

Please write out.

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.3 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 19 engines and the mean pressure was 4.5 pounds/square inch with a standard deviation of 0.8. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Based on extensive testing, a manufacturer of washing machines believes that the
distribution of the time (in years) until a major repair is required has a Weibull
distribution with alpa =2/3 and β=2.
a. What is the mean time until a major repair is required?
b. If the manufacturer guarantees all machines against a major repair for 1 year,
what proportion of all new washers will have to be repaired under the
guarantee?

Describe two research situations where discriminant analysis can be used: one situation where the primary interest is in group classification and another situation where the primary interest is in the description of the nature of group differences.

Please do all parts! Do not use statistics software. I want to see the formulas.

study of the effect of caffeine on muscle metabolism used 24 male volunteers who each underwent arm exercise tests. 12 of the men were randomly selected to take a capsule containing pure caffeine one hour before the test. The other men received a placebo capsule. During each exercise the subject's respiratory exchange ratio (RER) was measured. (RER is the ratio of CO2 produced to O2 consumed and is an indicator of whether energy is being obtained from carbohydrates or fats). The question of interest to the experimenter was whether, on average, caffeine changes RER. Data is in:

a. Construct a hypothesis test that detect whether there is difference in RER between two groups at .05 significant level (show steps)

b. Construct a hypothesis test that detect whether Caffeine reduces RER compared to placebo at .05 significant level (show steps)

54 randomly selected students were asked how many siblings were in their family. Let X - the number of pairs of siblings in the student's family.

Round all your answers to one decimal place.

The mean is:

The median is:

The sample standard deviation is:

The first quartile is:

The third quartile is:

What percent of the respondents have at least 1 siblings? _____%

88% of all respondents have fewer than how many siblings?

h² = 1 and that gene frequencies are known.

Assume you have 3 beef cows whose birth weights were as follows: A = 65 lbs, B = 75 lbs and C = 85 lbs. Your employer wants to breed only those cows which are more than 1 Standard Deviation above the population mean. If the population mean for birth weights, m_BW = 70 lbs, and the variance for birth weights, s²_BW = 64 lbs², how many of the cows should you select for breeding? Which ones specifically?

hint for this question-

1. m_BW + 1 S.D. =

2. A manufacturer of chocolate candies uses machines to package candies as they (4 pts) move along a filling line. The company wants the packages to contain 8.1730 ounces of candy. A sample of 50 packages is randomly selected periodically and the packaging process is stopped if there is evidence to show that the mean amount is different from 8.1730 ounces tested at a 95.00% confidence interval/level. In one particular sample of 50 packages, the MEAN.S is equal to 8.1590 ounces, with a STDEV.S of 0.0510 ounce - should the packaging process be halted? What will be the hypothesis in this study? What will be the area of rejection in this study using t Stat critical value? Create the statement of rejection or not-rejection based upon the t Stat value and the t Stat critical value What will be the conclusion of this study?