Assume that 20% of U.S. adults subscribe to the "five-second rule." That is, they would eat a piece of food that fell onto the kitchen floor if it was picked up within five seconds.

(1) Assuming this is a binomial situation, calculate the probability that more than 325 respondents in a survey of 1500 people, would subscribe to the five-second rule.

(Round your answer to the nearest 3 decimal places, show what you typed into the calculator,and define n, p, and r.)

(2) Provide evidence that conducting a normal approximation in this scenario would be appropriate.

(3) The survey went out to 1500 people . Calculate the mean and standard deviation.

(Label the mean and standard deviation clearly. Round to 3 decimal places where necessary.)

(4) Use the normal approximation method to answer the same question asked in part calculate the probability that more than 325 respondents in a survey of 1500 people would subscribe to the five-second rule. Show your work and round your answer to the nearest 3 decimal places.

(5) Your answers to questions 1 and 4 should have been fairly similar. Explain why your work in question 2 ensures that the probabilities you calculated using both methods would be close to one another.

Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint.

93 34 41 106 83 56 56 48 40 76 48 97 94 73 74 76 90 98 55 81

Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit (to 2 decimals).

Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal. What is the error bound of 95% confidence interval for the population mean length of engineering conferences? Construct a 95% confidence interval for the population mean length of engineering conferences. What is the lower bound? Construct a 95% confidence interval for the population mean length of engineering conferences. What is the upper bound?

Conduct a t-test for differences in weights between two groups of monkeys. Have group 1 as y and group 2 as x. What is the null hypothesis with evidence.

Give lower and upper values for the 95% confidence interval for the difference in means given by the t-test output. Are values similar to the output from an AVOVA or MCP test output ? If so, which values.

The values are

Group 1= 9.7, 9.5, 9.2, 8.5, 10.9, 9.8, 8.7, 9.8, 7.9, 9.0, 10.5, 8.9, 10.0, 8.9, 6.8, 8.2, 9.3, 10.5, 8.5, 9.4

Group 2= 8.1, 7.8, 7.6, 8.1, 9.9, 8.6, 8.8, 9.1, 10.4, 9.1, 6.9, 7.3, 6.7, 5.5, 9.6, 7.8, 8.7, 9.5, 7.8, 8.2

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of 2.0 liters and a standard deviation of 0.08 liter. Suppose you select a random sample of 25 bottles. a. What is the probability that the sample mean will be between 1.99 and 2.0 liters​? b. What is the probability that the sample mean will be below 1.98 liters​? c. What is the probability that the sample mean will be greater than 2.01 ​liters? d. The probability is 95​% that the sample mean amount of soft drink will be at least how​ much? e. The probability is 95​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)?

Of all cities in the United States, Amherst, New York, has the fewest number of days per year clear of clouds, 4.4. Other cities with very few clear days include Buffalo, New York, Lakewood, Washington, and Seattle, Washington. Suppose a random year is selected. (Round your answers to four decimal places.)

(a)

What is the probability that Amherst will have exactly four days clear of clouds?

(b)

What is the probability of fewer than six days clear of clouds?

(c)

What is the probability of at least nine days clear of clouds?

(d)

Suppose that between 2 and 11 (inclusive) days are clear of clouds. What is the probability of more than five days clear of clouds?

this is all the data provided for this question.

My Notes

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 45 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.20 ml/kg for the distribution of blood plasma.(a) Find a 90% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Use 2 decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is known

the distribution of weights is normal

σ is unknown

n is large

the distribution of weights is uniform

(c) Give a brief interpretation of your results in the context of this problem.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.10.

10% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.    

90% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.90.

(d) Find the sample size necessary for a 90% confidence level with maximal/marginal error of estimate E = 2.60 for the mean plasma volume in male firefighters.

Alice solves every puzzle with probability 0.6, and Bob, with probability 0.5. They are given 7 puzzles and each chooses 5 out of the 7 puzzles randomly and solves them independently. A puzzle is considered solved if at least one of them solves it. What is the probability that all the 7 puzzles happen to be solved by at least one of them?

A health psychologist tests a new intervention to determine if it can change healthy behaviors among siblings. To conduct the this test using a matched-pairs design, the researcher gives one sibling an intervention, and the other sibling is given a control task without the intervention. The number of healthy behaviors observed in the siblings during a 5-minute observation were then recorded.

Yes:6,4,7,7,7,5

No:5,6,5,6,5,5

Compute effect size using eta-squared. (Round your answer to two decimal places.)

Given two dependent random samples with the following results:

Population 1 32 35 45 46 43 45 30

Population 2 19 40 31 32 30 47 42

Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed.

Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

Step 2 of 4: Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4: Construct the 98% confidence interval. Round your answers to one decimal place.

a) The worksheet "Counts8Year" provides the number Top30 TV shows aired on each network by year. Run a two-way ANOVA without replication using the data in columns A to E of the "Counts8Year" worksheet. (Do not include row 1 and check labels.) Two hypothesis tests will be performed, one for the Year (row) factor and the other for the Network (column) factor. What is the value of the test statistic, F_calc, for the test on the Network factor? Provide your answer with 2 decimal places.

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b) R-square (R²) is the proportion of the variation in the data (number of top 30 shows) that can be explained by the factors (year and network). Compute R² = 1 - SSE/SST.   Provide your answer with 4 decimal places.  

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c) What is the conclusion of the ANOVA hypothesis test at a 5% significance level?  (Click to select)At least one pair of network means differ. At least one pair of the yearly means differ.None of the network means differ. None of the yearly means differ.All of the network means differ. All of the yearly means differ.None of the network means differ. At least one pair of yearly means differ.At least one pair of network means differ. None of the yearly means differ.None of the network means differ. All of the yearly means differ.All of the network means differ. None of the yearly means differ.

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d) Based on the ANOVA test results, which means are significantly different? (Click to select)Years 2015 and 2016ABC, CBSFOX, NBCCBS, NBCABC, FOXABC, NBCCBS, FOXNo pairs of means differ significantlyABC, CBS, FOX, NBC

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e) Which of the following methods/test would NOT be appropriate for testing the assumptions of this ANOVA test?

A simple random sample of 20 pages from a dictionary is obtained. The numbers of words defined on those pages are​ found, with the results nequals20​, x overbarequals54.3 ​words, sequals16.6 words. Given that this dictionary has 1477 pages with defined​ words, the claim that there are more than​ 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 47.4 words. Use a 0.10 significance level to test the claim that the mean number of words per page is greater than 47.4 words. What does the result suggest about the claim that there are more than​ 70,000 defined​ words? Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. Assume that the population is normally distributed.

It is known that of the articles produced by a factory, 20% come from Machine A, 30% from Machine B, and 50% from Machine C. The percentages of satisfactory articles among those produced are 95% for A, 85% for B and 90% for C. An article is chosen at random. (a) What is the probability that it is satisfactory? (b) Assuming that the article is satisfactory, what is the probability that it was produced by Machine A? (c) Given that the article is satisfactory, what is the probability that it was produced by Machine C?

Refer to the accompanying data set of mean​ drive-through service times at dinner in seconds at two fast food restaurants. Construct a 95​% confidence interval estimate of the mean​ drive-through service time for Restaurant X at​ dinner; then do the same for Restaurant Y. Compare the results.