Nike took a risk on Colin Kaepernick for its “Dream Crazy” #JustDoIt campaign. The first ad aired on national TV September 6, 2018. A year from now they will assess whether the risk paid off. To answer this question they will collect weekly sales data from September 6, 2018 – September 5, 2019 and compare it to 52 weeks of sales data over the previous year, September 6, 2017 to September 5, 2018. For each data point, they will record the date and sales. a. How would you analyze this data? • State the null and alternative hypothesis. • What statistical test would you use?

USING EXCEL The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is $29,858 (XO Group website, January 5, 2015). Assume that the cost of a wedding is normally distributed with a mean of $29,858 and a standard deviation of $5600. What is the probability that a wedding costs less than $20,000? What is the probability that a wedding costs between $20,000 and $30,000? For a wedding to be among the 5% most expensive, how much would it have to cost?

1. A researcher wants to determine whether the time spent online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Test the hypothesis that the time spent online per day is related to gender. Use α = 0.05.

1. Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.
2. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
3. Find the critical value(s) and identify the rejection region(s).
4. Find the appropriate standardized test statistic. If convenient, use technology.
5. Decide whether to reject or fail to reject the null hypothesis.
6. Interpret the decision in the context of the original claim.

a dice can have 6 sides and are numbered 1,2,3,4,5, and 6. The odds of getting an odd number are the same. The chance of getting an even number is the same. The chance of getting an odd number is twice the chance of getting an even number.
a. Determine the opportunity to get the number 3.
b. The dice is thrown three times. Determine the odds of getting two numbers 5 and one number 4.
c. The dice is tossed a hundred times. Use the approximation to determine the chances of getting an even number at most 37 times.

1. Andrew plans to retire in 38 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 38 years will exceed 12%?

2. Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ = 120 mg/dl and σ = 10 mg/dl.

(b) If measurements are made on 4 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?

discuss the sensitivity of outliers for mean, median, interquartile range, range, variance and standar deviation

Does gender influence the satisfaction reported by library patrons?

(a) " 18 women and 14 men reported that they were not satisfied with the library service.

(b) " 33 women and 20 men reported that they were satisfied.

(c) " 57 women and 85 men reported that they were very satisfied with the service.

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 211 accurate orders and 71 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: 0.226 < p < 0.323. What do you​ conclude? Need answer to both a. and b. Thanks.

The amount of contaminants that are allowed in food products is determined by the FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. Suppose you work for the FDA and are told that the current amount of somatic cells (common name "pus") in 1 cc of cow milk is currently 750,000 (note: this is the actual allowed amount in the US!). You are also told the standard deviation is 123000 cells. The FDA then tasks you with checking to see if this is accurate.

You collect a random sample of 55 specimens (1 cc each) which results in a sample mean of 782227 pus cells. Use this sample data to create a sampling distribution. Assume that the population mean is equal to the FDA's legal limit and see what the probability is for getting your random sample.

a. Why is the sampling distribution approximately normal?

b. What is the mean of the sampling distribution?

c. What is the standard deviation of the sampling distribution?

d. Assuming that the population mean is 750,000, what is the probability that a simple random sample of 55 1 cc specimens has a mean of at least 782227 pus cells?

e. Is this unusual? Use the rule of thumb that events with probability less than 5% are considered unusual.

f. Explain your results above and use them to make an argument that the assumed population mean is incorrect. (6 points) Structure your essay as follows:
Describe the population and parameter for this situation.

Describe the sample and statistic for this situation.

Give a brief explanation of what a sampling distribution is.

Describe the sampling distribution for this situation.

Explain why the Central Limit Theorem applies in this situation.

Interpret the answer to part d.

Use the answer to part e. to argue that the assumed population mean is either correct or incorrect. If incorrect, indicate whether you think the actual population mean is greater or less than the assumed value.

Explain what the FDA should do with this information.

A team of visiting polio eradication workers were informed during their orientation session that population-wide studies done in their host country showed that the risk of polio in villages of that country was strongly epidemiologically associated with the village’s economic/human development circumstances, which ranged greatly from village to village.  In some villages, residents lived in hand-constructed huts with no running water, no latrines or sewage disposal areas, and no electricity.  In other places, residents lived in wooden or adobe homes which, though modest by Western standards, had all of the above services in place and whose street side craft shops and food markets did a brisk business, catering both to locals and visitors.

Knowing this information, the team went into several villages and attempted to assign a “human development rating” to each family.  This was based on that family’s income situation, access to running water, access to elementary school for their children, and the condition of the home. To their surprise, they found that families in all the villages had no difference in polio risk based on the family’s human development rating.

Are steers and heifers equally distributed between angus and herefords

In a test of the Atkins weight loss program, 41 individuals participated in a randomized trial with overweight adults. After 12 months, the mean weight loss was found to be 2.1 Kg, with a standard deviation of 4.8 Kg. (a) What is the best point estimate for the mean weight loss of all overweight adults who follow the Atkins program? (b) Construct a 90% confidence interval for the mean weight loss for all such subjects? (c) Test the hypothesis that the mean weight loss is 3.2 Kg. (d) In part (c), could we conclude the test simply by looking at the confidence interval constructed in part (b)? Explain. Also, what is the minimum mean weight loss that would be rejected by the sample data? (e) Suppose that a weight loss program is considered effective only if the weight loss is at least 3.2 Kg after 12 months. Do you think, the Atkinson program seems to effective at 90% confidence level? (f) For part (e), could we use the confidence interval constructed in part (b)?

1. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 234 feet and a standard deviation of 58 feet. We randomly sample 49 fly balls.

b) What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.)

c) Find the 60th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)

4.The length of songs in a collector's iTunes album collection is uniformly distributed from two to 3.7 minutes. Suppose we randomly pick five albums from the collection. There are a total of 44 songs on the five albums.
d) Give the distribution of X (Round your answers to four decimal places.)

X ~ N ( 2.85 , ? )

e) Find the first quartile for the average song length. (Round your answer to two decimal places.)

f) Find the IQR (interquartile range) for the average song length. (Round your answer to two decimal places.)

6.The percent of fat calories that a person consumes each day is normally distributed with a mean of about 34 and a standard deviation of about ten. Suppose that 25 individuals are randomly chosen. Let

X = average percent of fat calories.

(a) Give the distribution of X. (Round your standard deviation to two decimal places.)

X ~ N ( 34, ? )

(c) Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.)

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,300. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)

(a) Find the 90^th percentile for an individual teacher's salary.

(b) Find the 90^th percentile for the average teacher's salary.

The function f ( x ) = 2 x 3 − 39 x 2 + 180 x + 3 f ( x ) = 2 x 3 - 39 x 2 + 180 x + 3 has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema. This function has a local minimum at x x = with output value: and a local maximum at x x = with output value. my open math.

University of Minnesota recently developed a new apple called First Kiss. At the Minnesota State Fair, 200 random fair goers sampled both the new apple and a Honeycrisp apple and asked which apple they preferred. Of the 200 people, 134 people preferred First Kiss and the remaining 66 people preferred Honeycrisp. Is there any preference between the two apples? Use α =0.05 to perform a 5-step test of hypothesis.