A recent study found that 61 children who watched a commercial for potato chips featuring a celebrity endorser ate a mean of 38 grams of potato chips as compared to a mean of 25 grams for 51 children who watched a commercial for an alternative food snack. Suppose that the sample standard deviation for the children who watched the​ celebrity-endorsed commercial was 21.1 grams and the sample standard deviation for the children who watched the alternative food snack commercial was 12.8 grams. Complete parts​ (a) through​ (c) below.

What is the test​ statistic?

Identify the​ p-value for this test from the technology​ output, rounding to three decimal places.

b. Assuming that the population variances are​ equal, construct a 95​% confidence interval estimate of the difference mu 1 minus mu 2 between the mean amount of potato chips eaten by the children who watched the​ celebrity-endorsed commercial and children who watched the alternative food snack commercial.determine the 95​% confidence interval using​ technology, rounding to two decimal places?

c. Compare and discuss the results of​ (a) and​ (b).

Marketing companies have collected data implying that teenage girls use more ring tones on their cellular phones than teenage boys do. In one particular study of 40 randomly chosen teenage girls and boys (20 of each) with cellular phones, the average number of ring tones for the girls was 3.4 with a standard deviation of 1.7. The average for the boys was 1.6 with a standard deviation of 0.7. Conduct a hypothesis test at the 5% level to determine if the averages are approximately the same or if the girls' average is higher than the boys' average. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

If you could tell me how to solve this on the tI-84 calculator that would be best thanks!

A) State the distribution to use for the test. (Enter your answer in the form zor t_dfwhere dfis the degrees of freedom. Round your answer to two decimal places.)

B) What is the p-value? (Round your answer to four decimal places.)

C) Explain what the p-value means for this problem.

D) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. (Upload your file below.)

Clark postulates that household size, respondents age and vulnerability index are covariates of monthly income. What are the various null hypotheses.

Suppose your hypothesis is that the average price of a two bedroom home in Little Rock is $150,000. You sample 10 homes and find an average price of $145000 with a standard deviation of 7,500. Set up the null hypothesis, and the alternate hypothesis (you can write this out in words). Show the test statistic, the critical statistic, and the results of your hypothesis test. (A) Test the hypothesis at the 10% significance level (B) Test the hypothesis at 5% significance level (C) Test the hypothesis at 1% significance level.

Assume that the GPA of a randomly chosen college student has a normal distribution with mean 2.84 and standard deviation 0.42.

a. Find the probability that a randomly chosen college student has a GPA of at least 2.30.

b. If then college students are independently selected, what is the probability that exactly nine of them have a GPA of at least 2.30.

1. There are 700 students in a middle school. At the end of the year, there is a school-wide drawing for 3 identical new bicycles.

1. Is this a combination or a permutation? Why?

2. How many possible outcomes of the drawing are there?

Suppose that bicycles in the drawing are not identical: One bike is plated in gold and valued significantly higher than the other two, the silver and bronze bikes, with the bronze being the cheapest.

3. Does this change the number of possible outcomes of the drawing? Explain.

Target versus Walmart: Who had the lowest prices? To address your consumer thirst for knowledge you identify 20 items (all brand-name items) currently on your household shopping list. You visit both your Local Target and Walmart, price each item, organize, and then store these data in TargetWalmart. Is there evidence to support that prices are cheaper at Walmart? (Use a 0.05 level of significance)

Please show me how to do this in excel using the data analysis tab

Hurricanes The data below represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.

Source: National Hurricane Center

• (a) Draw a scatter diagram treating atmospheric pressure as the explanatory variable.

• (b) determine the linear correlation coefficient between atmospheric pressure and wind speed.

• (c) Does a linear relation exist between atmospheric pressure and wind speed?

• D. Make sure that your scatter diagram includes a title and the axes are labeled.

3) [4] Below are the observed and expected (in parentheses) frequencies for athletic injuries for those athletes who properly stretched versus those who did not. Assuming a ? 2 Test for Independence test is being conducted, at ? = 0.05, are athletic injuries independent of stretching? Only list steps 3-7 of the hypothesis test.

Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use Minitab Express or StatKey include the appropriate output (copy + paste). If you do any hand calculations show your work using the Word equation editor. Clearly identify your final answers. Output without explanation will not receive full credit and answers with no output or explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board.

1. A team of researchers has developed a new weight loss supplement. They want to know if patients who use the new supplement for four weeks lose any weight. The supplement has some minor side effects including mild headaches and achiness. If the researchers obtain evidence of weight loss they will proceed to produce the supplement commercially and sell it for a large profit. If they do not obtain evidence of weight loss they will end the project. [70 points]

A. State the null and alternative hypotheses that the researchers should test. Use m_d to denote the mean weight loss computed as beginning weight minus final weight.

B. What does a Type I error mean in this situation? What are the consequences of making a Type I error here?

C. What does a Type II error mean in this situation? What are the consequences of making a Type II error here?

D. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your reasoning.

E. If you were working with this research team, what alpha level would you use? Explain your reasoning.

Assume that the research team completes this study with a sample size of 500 and finds a mean weight loss of 0.475 pound with a standard deviation of 3.978 pounds. Their p-value is 0.0039

F. Using the alpha level you selected in part E, are their results statistically significant? Explain why or why not.

G. Are their results practically significant? Explain why or why not.

2. The STAT 200 course coordinator wants to estimate the proportion of all online STAT 200 students who utilize Penn State Learning’s online tutoring services by either attending a live session or viewing recordings of sessions. In a survey of 80 students during the Fall 2018 semester, 29 had utilized their services. She used bootstrapping methods to construct a 95% confidence interval for the population proportion of [0.263, 0.475]. Use this information to address the following questions. [30 points]

A. Supposed the coordinator decides that she wanted to conduct a hypothesis test instead. She wants to know if the proportion who utilize Penn State Learning’s online tutoring services is different from 0.25. What would be the appropriate null and alternative hypotheses?

B. Based on the 95% bootstrap confidence interval, would you expect the coordinator to reject or fail to reject the null hypothesis from part A at the 0.05 alpha level? Do NOT conduct the hypothesis test; use the confidence interval given in the question. Explain your reasoning.

C. Using this scenario, compare and contrast confidence intervals and hypothesis testing. List at least one similarity and at least one difference.

(A) A gum ball dispenser contains a large number of gum balls in three different colors, red, green, and yellow. Assuming that the gum balls are dispensed one at a time, describe an appropriate sample space for this scenario and list all possible events. Adetermined child continues to buy gum balls until he gets a yellow one. Describe an appropriate sample space in this case. (B) A brother and a sister arrive at the gum ball dispenser of the previous question, and each of them buys a single gum ball. The boy always allows his sister to go first. Let A be the event that the girl gets a yellow gum ball and let B be the event that at least one of them gets a yellow gum ball. (a) Describe an appropriate sample space in this case. (b) What outcomes constitute event A? (c) What outcomes constitute event B? (d) What outcomes constitute event A ∩ B? (e) What outcomes constitute event A ∩ Bc? (f) What outcomes constitute event B − A?

The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest. 16; 17; 19; 20; 20; 21; 22; 23; 24; 24; 24; 25; 25; 26; 26; 26; 27; 28; 29; 32; 33; 33; 34; 35; 37; 39; 40

a. Find the sample mean ?̅.

b. Find the mode.

c. Find the first quartile.

d. Find the median.

e. Find the third quartile.

f. Construct a box plot.

g. What percent of people surveyed visited a store at least 3 times?

h. Find the 40th percentile. i. Construct a histogram of the data.

j. Find the percentile of data point 29.

k. State whether the data are symmetrical, skewed to the left, or skewed to the right.

l. Find the sample standard deviation.

Use the magnitudes​ (Richter scale) of the earthquakes listed in the data set below. Find the mean and median of this data set. Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier​ (data value that is very far away from the​ others) when considered in the context of the sample data given in this data​ set? Explain. Find the mean and median of the data set using a calculator or similar data analysis technology.

2.83 0.48 1.95 0.59 2.78 1.34 0.04 0.83 0.96 0.36

1.36 1.81 2.67 1.53 2.66 1.39 0.99 0.38 2.44 0.33

2.93 1.07 2.61 0.01 1.18 2.35 1.06 2.78 2.47 0.54

2.18 2.94 0.37 1.95 2.79 1.57 2.82 0.76 2.96 2.98

2.13 1.04 0.17 1.78 0.98 2.72 1.99 1.35 1.73 0.03

Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier when considered in the context of the sample data​ given?

A sample of 16001600 computer chips revealed that 21%21% of the chips fail in the first 10001000 hours of their use. The company's promotional literature states that 23%23% of the chips fail in the first 10001000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Is there enough evidence at the 0.020.02 level to support the manager's claim?

signifigant evidence or not enough evidence

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property it can then be sold for $160,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $150,000.

Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $130,000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $130,000? Round your answer to 1 decimal place. Enter your answer as a percent. ___________%

Use the simulation model to compute the profit for each trial of the simulation run. With maximization of profit as Strassel’s objective, use simulation to evaluate Strassel’s bid alternatives of $130,000, $140,000, or $150,000. What is the recommended bid, and what is the expected profit? A bid of $140,000 results in the largest mean profit of $ _________________.