3. Estimate Interval The makers of a soft drink want to identify the average age of its consumers. A sample of 61 consumers was taken. The average age in the sample was 23 years with a sample standard deviation of 5 years. Please answer the following questions: a. Construct a 95% confidence interval estimate for the mean of the consumers’ age. b. Suppose a sample of 85 was selected (with the same mean and the sample standard deviation). Construct a 95% confidence interval for the mean of the consumers’ age.

[Hint: Please see Chap008 – Slides 24-29 for formula and example. Please also see page 343-349 in the textbook.]

4. Hypothesis Testing Annual per captial consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the Midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a sample standard deviation of s=4.8. a. Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean. b. At α=0.05, test for a significant difference. What is your conclusion? Extra credit 5. A lathe is set to cut bars of steel into lengths of 9 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 9 centimeters. A sample of 100 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 9.085 centimeters. Suppose the population standard deviation is 0.335 centimeters. a. Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment. b. Compute the test statistic. c. Using the p-value approach, what is your conclusion? Let α = .05.

The mileage of the hybrid car, the Honda Insight, is normally distributed with a mean of 63.4 mpg and a standard deviation of 12.6 mpg.

1. Is it possible to find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg? Provide a justification for your answer.

2. If we want to address the problem “Find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg”, write the probability statement.

3. If we want to address the problem “Find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg”, what is the probability? Be sure to show how you calculated your probability.

This example was previously posted, but how did we come up with a Q1 result of 28.5 and a Q3 result of 123.3 for the question below? I am wondering where I went wrong here, as the results to this question have already been posted. The results I have are Q1 of 29 and Q3 of 121 with a median of 69. I have IQR as 92 and for outliers I have -109 for lower limit and 259 for upper limit. I am wondering how we came up with 28.5 for Q1 and 123.3 for Q3. Once I understand this, then figuring out IQR and outlier limits makes sense.

Hospital - Infections

Consider the following hypotheses:

H₀: μ = 470
H_A: μ ≠ 470

The population is normally distributed with a population standard deviation of 44. (You may find it useful to reference the appropriate table: z table or t table)

a-1. Calculate the value of the test statistic with x−x− = 483 and n = 65. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  
Test statistic = ?

a-2. What is the conclusion at the 10% significance level?
  

A) Do not reject H₀ since the p-value is greater than the significance level.

B) Do not reject H₀ since the p-value is less than the significance level.

C) Reject H₀ since the p-value is greater than the significance level.

D) Reject H₀ since the p-value is less than the significance level.

a-3. Interpret the results at αα = 0.10.

A) We cannot conclude that the population mean differs from 470.

B) We conclude that the population mean differs from 470.

C) We cannot conclude that the sample mean differs from 470.

D) We conclude that the sample mean differs from 470.

b-1. Calculate the value of the test statistic with x−x− = 438 and n = 65. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  
Test statistic = ?

b-2. What is the conclusion at the 5% significance level?
  

A) Reject H₀ since the p-value is greater than the significance level.

B) Reject H₀ since the p-value is less than the significance level.

C) Do not reject H₀ since the p-value is greater than the significance level.

D) Do not reject H₀ since the p-value is less than the significance level.

b-3. Interpret the results at αα = 0.05.

A) We conclude that the population mean differs from 470.

B) We cannot conclude that the population mean differs from 470.

C) We conclude that the sample mean differs from 470.

D) We cannot conclude that the sample mean differs from 470.

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 117 and a standard deviation of about 45. Assume forty-seven individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) For the group of 47, find the probability that the average number of friends is more than 121. Find the third quartile for the average number of Facebook friends. For part b), is the assumption that the distribution is normal necessary? NoYes

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. LOADING... Click the icon to view the table. a. State the multiple regression equation. Let Upper X Subscript 1 i represent the alcohol content​ (%) of wine i and let Upper X Subscript 2 i represent the number of chlorides for wine i. Quality Alcohol_Content(%) Chlorides 0 7.9 0.067 1 7.1 0.062 2 8.9 0.067 2 8.1 0.071 2 8.6 0.073 3 8.9 0.074 2 9.3 0.072 5 9.5 0.077 6 10.4 0.077 7 10.3 0.079 7 10.1 0.083 6 10.9 0.084 7 11.4 0.081 7 11.4 0.084 6 11.9 0.095 9 11.5 0.096 8 11.7 0.119 9 11.5 0.143 10 12.3 0.151 9 12.3 0.159 b. Interpret the meaning of the​ slopes, b 1 and b 2​, in this problem. c. Explain why the regression​ coefficient, b 0​, has no practical meaning in the context of this problem. c. Predict the mean quality rating for wines that have 8​% alcohol content and chlorides of 0.10. d. Construct a​ 95% confidence interval estimate for the mean quality rating for wines that have 8​% alcohol and 0.10 chlorides. e. Construct a​ 95% confidence interval estimate for the mean quality rating for wines that have 8​% alcohol and 0.10 chloride Construct a​ 95% prediction interval estimate for the quality rating for an individual wine that has 8​% alcohol and 0.10 chlorides. h. What conclusions can you reach concerning this regression​ model?

Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 204 women, r₁ = 56 responded yes. Another random sample of n₂ = 193 men showed that r₂ = 47 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use α = 0.10. Solve the problem using both the traditional method and the P-value method. (Test the difference p₁ − p₂. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.)

Conclusion

Fail to reject the null hypothesis, there is sufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.Reject the null hypothesis, there is sufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.    Reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.Fail to reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.

Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.These two methods differ slightly.    The conclusions obtained by using both methods are the same.We reject the null hypothesis using the traditional method, but fail to reject using the P-value method.

From 1984 to 1995 , the winning scores for a golf turnament were 276,279,279,277,278,278,280,282,285,272,279 and 278. Using the standart deviation from this sample find the percent of winning scores that fall within one standart deviation of the mean.

Use the calculator provided to solve the following problems.

Consider a t distribution with 16 degrees of freedom. Compute P (t ≥ 1.10)
Round your answer to at least three decimal places.

Consider a t distribution with 28 degrees of freedom. Find the value of c such that P(-c < t < c) =0.99
Round your answer to at least three decimal places.

P (t ≥1.10) =

c=

Three students, Linda, Tuan, and Javier, are given laboratory rats for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 0.05, test the hypothesis that the three formulas produce the same mean weight gain.

H₀: μ₁ = μ₂ = μ₃
H_a: At least two of the means differ from each other

Run a single-factor ANOVA with α=0.05

. Round answers to 4 decimal places.

Test Statistic =
p-value =

Based on the p-value, what is the conclusion

Reject the null hypothesis: at least one of the group means is different

Fail to reject the null hypothesis: not sufficient evidence to suggest the group means are different

A football receiver, Harvey Gladiator, is able to catch two thirds of the passes thrown to him. He must catch four passes for his team to win the game. The quarterback throws the ball to Harvey six times. (a) Find the probability that Harvey will drop the ball all six times. (b) Find the probability that Harvey will win the game. (c) Find the probability that Harvey will drop the ball at least two times.

A radio station runs a promotion at an auto show with a money box with 14 ​$50 ​tickets, 10 ​$25 ​tickets, and 15 ​$5 tickets. The box contains an additional 20 ​"dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that all three tickets have no value. The probability that all three tickets drawn have no money value is nothing. ​(Round to four decimal places as​ needed.)

Tommy has a bag with 7 marbles in it, and decides to draw 3 marbles from the bag randomly. The marbles in the bag are all the same, but some of the marbles in the bag are red and some are purple. If we decide to test the null hypothesis "More red marbles than purple marbles" and the alternative hypothesis "More purple marbles than red marbles", what would be the level of significance? We will make the Rejection Region the event of getting atleast 2 marbles that are purple.

1. In many animal species the males and females differ slightly in structure, coloring, and/or size. The hominid species Australopithecus is thought to have lived about 3.2 million years ago. (“Lucy,” the famous near complete skeleton discovered in 1974, is an Australopithecus .) Forensic anthropologists use partial skeletal remains to estimate the mass of an individual. The data below are estimates of masses from partial skeletal remains of this species found in sub-Saharan Africa. Appropriate graphical displays of the data indicate that it is reasonable to assume that the population distributions of mass are approximately normal for both males and females. You may also assume that these samples are representative of the respective populations. Estimates of mass (kg)

Males 51.0, 45.4, 45.6, 50.1, 41.3, 42.6, 40.2, 48.2, 38.4, 45.4, 40.7, 37.9, 41.3, 31.5

Females 27.1, 33.5, 28.0, 30.3, 32.7, 32.5, 34.2, 30.5, 27.5, 23.3,35.7

Do these data provide convincing evidence that the mean estimated masses differ for Australopithecus males and females? Provide appropriate statistical justification for your conclusion.

2. In an introductory marketing class students were presented with 6 items they could bid on in an auction. They were asked to bid privately and also estimate the “typical” bid for each item by their classmates. The items were randomly selected from a large list of items that students might purchase. An initial analysis of the data established the plausibility that the distribution of differences (estimated – actual) is approximately normal.

Construct a 95% confidence interval for the mean difference between the actual bid and the estimated “typical” bid for the population of items.

Use the table above to answer the following questions. Show ALL of your work for full credit.

1. Calculate the mean, median, and mode cost of last month’s expenses.

2. Calculate the range and interquartile range (IQR) of last month’s expenses.

Remember, to find the IQR:

Step 1: Put the numbers in order.

Step 2: Find the median.

Step 3: Place parentheses around the numbers above and below the median.
Step 4: Find Q1 and Q3

Step 5: Subtract Q1 from Q3 to find the interquartile range.

3. Which of the expenses (if any) in the table above is an outlier? Why?

Remember, an outlier is defined as being any point of data that lies over 1.5 IQRs below the first quartile (Q1) or above the third quartile (Q3) in a data set.

High = (Q3) + 1.5 IQR

Low = (Q1) – 1.5 IQR

4. Find the variance and standard deviation. How many standard deviations is the cost of the mortgage payment from the mean cost of all expenses.

5. Explain the difference between the mean and the median. Also, indicate whether the data is skewed or not. Why?

I need help finding number 3 and 4! I believe the range is 1727 and the IQR is 441, but what is the outliers, variance and standard deviation?