For a data set obtained from a sample, n=75 and x¯=47.80. It is known that σ=3.8.

a. What is the point estimate of μ?

The point estimate is .

b. Make a 90% confidence interval for μ.

Round your answers to two decimal places.

(,)

c. What is the margin of error of estimate for part b?

Round your answer to three decimal places.

E=

1. In an International Mass Retail Association survey of 1006 U.S. households, 324 of the households said that Saturday is their favorite shopping day (USA Today, October 6, 1993). Construct a 95% confidence interval for the proportion of all U.S. households for whom Saturday is their favorite shopping day. Round your answer to three decimal places.

A sample of 130 working students at a large university was asked how many hours they work in a typical week. A 95% z confidence interval for the average number of hours a week a typical student employee works was (13.5, 15.3)

(a)Identify each of the following interpretations as TRUE or FALSE with a brief explanation for each.

i. 95% of sampled student workers work between 13.5 and 15.3 hours in a typical week.

ii. We are 95% confident that the average numbers of hours a students employee works in a typical week is between 13.5 and 15.3.

iii. We can be confident that about 95% of all student workers work between 13.5 and 15.3 hours in a typical week.

iv. This interval was constructed in such a way that around 95% of all intervals similarly constructed would capture the population average number of hours a week a typical student employee works

(b)Calculate the sample mean and sample standard deviation that were used to build the confidence interval. Show your work.

Suggest one or more types of graph that would be appropriate for showing an association between each of the following variables. If more than one type is appropriate, indicate what additional factors would influence your choice, if any. (One mark each).

a) Plant height (cm) and fertilizer type (N, P or K)

b) The proportion of tadpoles surviving to adulthood and the concentration of a pesticide in the environment

c) The proportion of individuals contracting seasonal flu and the vaccination status of individuals (had or did not have the flu shot)

d) The average adult body size of mammal species (kg) and the average size of their home range (km2)

e) The number of viable eggs produced by hermaphroditic worms and the way in which the eggs were fertilized (self-fertilization or fertilization by another worm).

Suppose a government official wants to know what proportion of residents are infected with the an illness. There are a limited number of tests. So a random sample of 180 residents was taken, and these residents were tested for the illness. Of these 180 people, 36 were found to be infected with the illness. a) Find a 95% confidence interval for the true proportion of residents who are infected. b) a healthcare professional says they suspect that fewer than 30% of residents were infected at that time. Use a hypothesis test ( significance level=0.01) to determine if this statement is supported by the data and be sure to show the sample size is large enough to make estimates in the analysis.

Test a model that tries to explain differences in BMI based on parents' average BMI, a person's age, number of weekly hours of exercise, and the number of times a person eats outside.

Which independent variable (IV) does not explain variability in a person's BMI? Explain.

A dolphin trainer wants to test the effect of food motivation on the ability for captive dolphins to learn tricks.  She studies a sample of dolphins from Sea World and randomly assigns individuals to one of three food motivation conditions: low, moderate or high.  The level of food motivation corresponds to the type of food given to the dolphins during training: a low-preference food, a moderately-preferred food, or a highly-preferred food.  Dolphins are trained to jump through hoops in their pool and are rewarded with one of the three types of food.  The trainer then measures the number of hoops successfully jumped the day after the training session.

The data for the three food motivation conditions are below.

Complete the following calculations BY HAND:

a. State the null and alternative hypotheses and identify the critical value of F.

b.  Calculate SS Total, SS Between, and SS Within.  Also calculate df Total, df Between and df Within.

c.  Calculate MS Between and MS Within.  Calculate the observed F-ratio, and create an ANOVA source table for the analysis.  

d.  What is your decision regarding the null hypothesis?  State the results of the main ANOVA in nonstatistical terms.

e.  Calculate the Tukey critical value for the analysis.  Which food motivation conditions significantly differ from one another?

f. Write a very short paragraph (2 - 3 sentences) summarizing your ANOVA and Tukey results in APA format

Virus Z is a new virus infecting people. Some people get Virus Z and develop no systems. In others, Virus X causes a disease called Disease Z.

If you have Virus Z, you have it for life and everyone you touch gets Virus Z, if they didn’t have it already. (They get it immediately when you touch them.) If you get Virus Z, you will either immediately develop Disease Z, or you will never develop Disease Z, and those two outcomes are equally likely. Different people’s reactions to the virus are independent.

There is a 50% chance John has Virus Z. John does not have Disease Z. John touches four people without Virus Z. Given that the first three do not develop Disease Z, what is the probability that the fourth one develops Disease Z?

The number of loaves of bread sold per day by an organic bakery over the past five years can be treated as a random variable that is normally distributed. This distribution has a mean of 77.5 and a standard deviation of 14.4 loaves. Suppose a random sample of 36 days has been selected. Determine the probability that the average number of loaves sold in the sample of days exceeds 80 loaves. First find the standard error of the mean.

Now calculate the Z (Standard) Score. Round your answer to two decimal places

Now find the probability that the average number of loaves sold in the sample of days exceeds (is greater than) 80 loaves.

Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per person in traffic delays. A random sample of eight cities showed the following data. x (hr) 29 5 22 38 23 25 16 5 y (gal) 49 3 35 55 31 37 27 9 (a) Draw a scatter diagram for the data. Get Flash Player Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. Verify that Σx = 163, Σx2 = 4229, Σy = 246, Σy2 = 9800, and Σxy = 6411. Compute r. The data in part (a) represent average annual hours lost per person and average annual gallons of fuel wasted per person in traffic delays. Suppose that instead of using average data for different cities, you selected one person at random from each city and measured the annual number of hours lost x for that person and the annual gallons of fuel wasted y for the same person. x (hr) 22 4 19 43 16 25 2 39 y (gal) 65 8 10 52 25 34 4 71 (b) Compute x and y for both sets of data pairs and compare the averages. x y Data 1 Data 2 Compute the sample standard deviations sx and sy for both sets of data pairs and compare the standard deviations. sx sy Data 1 Data 2 In which set are the standard deviations for x and y larger? The standard deviations for x and y are larger for the first set of data. The standard deviations for x and y are larger for the second set of data. The standard deviations for x and y are the same for both sets of data. Look at the defining formula for r. Why do smaller standard deviations sx and sy tend to increase the value of r? Multiplying by smaller numbers results in a smaller value. Dividing by smaller numbers results in a larger value. Multiplying by smaller numbers results in a larger value. Dividing by smaller numbers results in a smaller value. (c) Make a scatter diagram for the second set of data pairs. Get Flash Player Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. Verify that Σx = 170, Σx2 = 5116, Σy = 269, Σy2 = 13,931, and Σxy = 7915. Compute r. (d) Compare r from part (a) with r from part (b). Do the data for averages have a higher correlation coefficient than the data for individual measurements? Yes, the data for averages have a higher correlation coefficient than the data for individual measurements. No, the data for averages do not have a higher correlation coefficient than the data for individual measurements. List some reasons why you think hours lost per individual and fuel wasted per individual might vary more than the same quantities averaged over all the people in a city. This answer has not been graded yet.

State Farm Insurance studies show that in Colorado, 55% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 9 property damage claims involving automobiles are selected at random.

(a) Let r be the number of claims made by males under age 25. Make a histogram for the r-distribution probabilities.

(b) What is the probability that four or more claims are made by males under age 25? (Use 3 decimal places.)


(c) What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution? (Use 2 decimal places.)

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 56 and estimated standard deviation σ = 25. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)

- What is the probability that x < 40? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

(e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?

The J.R. Ryland Computer Company is considering a plant expansion to enable the company to begin production of a new computer product. The company’s president must determine whether to make the expansion a medium- or large-scale project. Demand for the new product is uncertain, which for planning purposes may be low demand, medium demand, or high demand. The probability estimates for demand are 0.20, 0.20, and 0.60, respectively. Letting x and y indicate the annual profit in thousands of dollars, the firm’s planners developed the following profit forecasts for the medium- and large-scale expansion projects.

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1421 referee​ calls, with the result that 428 of the calls were overturned. Women challenged 748 referee​ calls, and 230 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (c) below.