Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 14 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.20 gram.

(a)

Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

lower limit

upper limit

(b)

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

normal distribution of weightsn is largeuniform distribution of weightsσ is unknownσ is known

(c)

Interpret your results in the context of this problem.

We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.     The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.

(d)

Find the sample size necessary for an 80% confidence level with a maximal margin of error  E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

Historically, weights of polar bears have been known to be Normally Distributed with a population mean of approx. 550 kg and a standard deviation of about 110 kg. Researchers are studying the effect of climate change on these animals; their hypothesis is that, because of the diminishing size of their feeding habitats, the average polar bear will be smaller than in the past.

1.) What is the probability that a randomly selected polar bear would weigh less than 480 kg? Would this be an unusual event?

2.) Suppose researchers plan to take a random sample of 20 polar bears and calculate their sample mean. Would this sample mean be the same with every sample? Why or why not? Describe the sampling distribution of the sample mean weight, being sure to address the issue of Center, Shape, and Spread.

3.) What is the probability that a random sample of 20 polar bears would have a mean weight of 500 kg or less? Would this be an unusual event- that is, if we got a sample mean of 500 kg or less, would this be rare or would it be relatively commonplace?

1.A quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. Production runs are done 10 hours a day, 7 days a week. The dependent variable is ______.

b) number of production runs
c) number of defects
d) production run
e) percentage of defects


2) In the equation y = m x + b, which represents a straight lime, b is the __________.
a) slope of the line
b) origin
c) y-intercept of the line
d) x-intercept of the line


3) Determine the Pearson product-moment correlation coefficient for the following data.
x 1 11 9 6 5 3 2
y 10 4 4 5 7 7 9

Gillette claims that their double-edge shaver is better than the leading brand of single-edge shavers (Lady Bic). In a recent study, 26 women rated the Gillette and the Lady Bic shavers on smoothness, closeness and safety. One group of women were used and each woman recorded two scores. The mean difference of those scores were tested with the following results.

Critical Value…………… t = 1.645

Test statistic ..................... t = 1.978

P-value.............................. = . 031

Significance level ……........... = .05

What type of conclusion error could be made using the results of this study?

                 a) type II                b)   none            c) type III                            d) type I

Foot Locker uses sales per square foot as a measure of store productivity. Last year, the mean annual sales per square foot was $370 with a standard deviation of $38.54. Suppose you take a random sample of 64 Foot Locker stores operating last year. There is a 86% probability that the sample mean annual sales per square foot is at least $______. a. None of the answers is correct b. 375.2029 c. 364.7971 d. 328.3768 e. 411.6232

The production of wine is a​ multibillion-dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine​ experts, data was collected from red wine variants. A sample of 20 wines is provided in the accompanying table. Develop a multiple linear regression model to predict wine​ quality, measured on a scale from 0​ (very bad) to 10​ (excellent) based on alcohol content​ (%) and the amount of chlorides. Complete parts a through g below.

Quality   Alcohol_Content(%)   Chlorides
2   7.7   0.067
1   7.9   0.065
3   8.2   0.074
1   8.7   0.071
2   8.5   0.067
4   8.7   0.074
4   9.4   0.071
3   9.1   0.076
6   10.1   0.077
5   10.4   0.078
7   10.3   0.078
6   11.1   0.083
7   11.3   0.081
8   11.5   0.085
6   11.8   0.095
7   11.3   0.093
7   12.5   0.128
8   11.5   0.111
10   12.2   0.157
10   12.8   0.156

1. Construct a​ 95% confidence interval estimate for the mean quality rating for wines that have 11​% alcohol and 0.08 chlorides.

2. Construct a​ 95% prediction interval estimate for the quality rating for an individual wine that has 11​% alcohol and 0.08 chlorides.

In a survey of 28 teenagers who were asked how many hours per week they spend watching T.V., the sample mean was 13 hours and the population standard deviation is 5.8 hours. Find a 99% Confidence Interval for the population mean number of hours teenagers watch T.V.

Write the interval below. Write a sentence interpreting this. (Round answer to 2 decimal places)

15.What kind of information is contained in the bottom box of information? (has Equality of Variances in the upper middle of box)

Select one:

a. Location information on the two populations.

b. Validity information on the hypothesis test.

c. Spread information on the two populations.

d. Descriptive information on the two samples.

16.What kind of information is contained in the third box of information? (has Pooled and Satterthwaite in the left side of box)

Select one:

a. Validity information on the hypothesis test.

b. Location information on the two populations.

c. Descriptive information on the two samples.

d. Spread information on the two populations.

17.What is the null hypothesis of Levene's Equality of Variances hypothesis test?

Select one:

a. H₀: The samples are equal.

b. H₀: The populations are equal.

c. H₀: The population variances are equal.

d. H₀: The population means are equal.

18.What is the null hypothesis of the two-sample independent t-test?

Select one:

a. H₀: The population means are equal.

b. H₀: The population variances are equal.

c. H₀: The samples are equal.

d. H₀: The populations are equal.

19.Which row of the two-sample independent t-test output is used if the Equality of Variance p-value = 0.08?

Select one:

a. The row for The Equal Variances.

b. The row for the Satterthwaite Method.

c. The row for the Pooled Method.

d. The row for the Folded F Method.

20.Looking at the output for the two-sample independent t-test, are the population spreads for Bush and Gore equal?

Select one:

a. No, because the S-W p-values for Bush and Gore are both less than 0.05.

b. Yes, because we always assume equality of variances for two-sample, independent t-tests.

c. Yes, since the sample sizes for both Bush and Gore is 50, which is greater than 30.

d. No, since the p-value in the Folded F row is less than 0.05.

21.Looking at the output for the two-sample independent t-test, which p-value tests whether the mean number of votes for Bush and Gore are equal?

Select one:

a. 0.4563

b. 0.9124

c. 0.9125

d. 0.0309

The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute.

(i) What is the probability of no views in a minute?

(ii) What is the probability of two or fewer views in 10 minutes?

(iii) What is the probability of two or fewer views in 2 hours?

A simple random sample of 90 items from a population with σ = 7 resulted in a sample mean of 33. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean. to

b. Provide a 95% confidence interval for the population mean. to

c. Provide a 99% confidence interval for the population mean.

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows.

Brand Price Score

Bose 180 76

Scullcandy 150 77

Koss 85 68

Phillips/O'Neill 80 58

Denon 70 40

JVC 35 27

a. Does the t test indicate a significant relationship between price and the overall score? The test t-Conclusion at α = .05 t = (to 2 decimal places.) p-value is What is your conclusion? Use α = .05. .

b. Test for a significant relationship using the F test. p-value is What is your conclusion? Use α = .05. Because p-value is .05, we H0: β1 is .

c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary.

Source of Variation

Sum of Squares

Degrees of Freedom

Mean Square F

p-value

Regression Error Total

Perform a between-groups ANOVA on the provided data set. What are your hypotheses? What do you conclude from your analysis? Be sure to show all work.

Major GPA Business 3.0 Business 3.3 Business 3.1 Business 3.2 Psychology 3.9 Psychology 4.0 Psychology 3.3 Psychology 3.7 History 3.8 History 3.6 History 3.7 History 3.5

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228 customers on the number of hours cars are parked and the amount they are charged.

Click here for the Excel Data File

a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

a-2. Is this a discrete or a continuous probability distribution?

Discrete

Continuous

b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

b-2. How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

Find the mean and the standard deviation of the amount charged. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

rev: 10_12_2018_QC_CS-142885