Describe the difference you would expect to see in the values of the mean and median for

a normal distribution, a positively skewed distribution, and a negatively skewed

distribution.

Use the following information for questions 1-5.

Do larger families spend more per week on food? A sample of 10 families in Chicago revealed the following data for family size and the weekly grocery bill. (Part of the calculations are done for you.)

           Family size     $Groceries     (X-Xbar)        (Y-Ybar)       (X-Xbar) x (Y-Ybar)

•          3                 99                -1                 -11                        11
•          6                114                2                    4                          8
•          5                131                1                   21                       21
•          6                129                2                   19                       38
•          6                142                2                   32                       64
•          3                111               -1                    1                       
•          4                104                0
•          2                  81
•          2                  98
•          3                  91
•         40             1100

Sx = 1.63     Sy = 19.28     X-bar = 40/10 = 4    Y-bar = 1100/10 = 110

Grocery Question #1: Calculate ∑ (X - Xbar) x (Y - Ybar)

Grocery Question #2: Assuming that ∑ (X - Xbar) x (Y - Ybar) is equal to 242, calculate r.

Grocery Question #3: Assuming that r = +0.856, determine the regression equation,

Grocery Question #4: Assuming that the Regression equation is Y = 70 + .858X, how much would you expect a family of five to spend on groceries over a week's time?

Grocery Question #5: Assuming that the coefficient of determination is 0.732, what conclusion can you reach?

A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

Complete the ANOVA table. Use 0.05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places.)

Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)

Men’s heights are normally distributed with a mean of 72 inches and a standard deviation of 3.1 inches. A social organization for short people has a requirement that men must be at most 66 inches tall. What percentages of men meet this requirement? Choose the correct answer:

A-2.62%

B-2.59%

C-2.56%

D-2.68%

Find the critical value of t for a sample size of 24 and a 95% confidence level. Choose the correct value from below:

A-2.096

B-2.064

C-2.046

D-2.069

Construct a confidence interval for the population mean using a t-distribution:

c = 99% m = 16.7 s = 3.2 n = 20. Choose from the intervals listed below.

A-(14.563, 18.474)

B-(14.664 18.736)

C-(14.653, 18.747)

D-(14.646, 18.763)

Assume that adults have IQ scores that are normally distributed, with a mean of 107 and a standard deviation of 15. Find the probability that a randomly selected individual has an IQ between 75 and 117. Choose the correct value:

A-0.7318

B-0.7155

C-0.7320

D-0.7167

In a survey, 376 out of 1,078 US adults said they drink at least 4 cups of coffee a day. Find a point estimate (P) for the population proportion of US adults who drink at least 4 cups of coffee a day, then construct a 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day.

A-P=0.0374; (31.14%, 38.26%)

B-P=0.3488; (32.03%, 37.72%)

C-P=0.3488; (32.49%, 37.88%)

D-P=0.3488; (31.14%, 38.62%)

Your firm wants to investigate how much money the typical tourist will spend on their next visit to New York. How many tourists should be included in your sample if you want to be 90% confident that the sample mean is within $17 from the population mean? From previous studies, we know that the standard deviation is $70.

A-45

B-46

C-47

D-48

The mean rent of a 3-bedroom apartment in Orlando is $1200. You randomly select 12 apartments around town. The rents are normally distributed with a standard deviation of $300. What is the probability that the mean rent is more than $1100?

A-0.1827

B-0.8173

C-0.1251

D-0.8749

A study of women’s weights found that a randomly selected sample of 150 women had a mean weight of 147.3 lb. Assuming that the population standard deviation is 19.6 lb., construct a 95% confidence interval estimate of the mean weight of all women. Choose the correct interval from below:

A-(144.211, 150.389)

B-(140.611, 146.789)

C-(144.667, 149.933)

D-(144.163, 150.437)

A music industry researcher wants to estimate, with a 90% confidence level, the proportion of young urban people (ages 21 to 35 years) who go to at least 3 concerts a year. Previous studies show that 35% of those people (21 to 35 year olds) interviewed go to at least 3 concerts a year. The researcher wants to be accurate within 2% of the true proportion. Find the minimum sample size necessary.

A -2185

B-1539

C-2401

D-8740

A researcher fails to find a significant difference in mean blood pressure in 36 matched pairs. The test was carried out with a power of 85%. Assuming that this study was well designed and carried out properly, do you believe that there really is no significant difference in blood pressure? Explain your answer.

I just really need this question explained to me in words I can understand. I have zero statistics background. Thanks

Bloomberg Media Group reported the result of an internet survey of 1000 New Yorkers.
The key question asked was: "Should a wealth tax be levied to pay for humanitarian relief efforts?". The results of the survey were as follows:

Is this enough evidence to draw the conclusion that the two groups i.e. Urban and Rural differ significantly with respect to their opinions? (Test at 5% level of significance)

The number of hours per week that high school seniors spend on computers is normally distributed with a mean of 5 hours and a standard deviation of 2 hours. 70 students are chose at random, let x̅ represent the mean number of hours spent on a computer for this group. Find the probability that x̅ is between 5.1 and 5.7.

Consider a portfolio investment consisting of 40% invested in MTN, 60% invested in Multichoice
Additional information:
Expected return:
MTN : -0,001986441
Multichoice: 0,003255932

3.1 Calculate the expected return of the portfolio
3.2 Calculate the covariance of the portfolio
3.3 Calculate the variance of the portfolio and standard deviation of the portfolio
3.4 Given that the risk free rate is 0.0002. Calculate the Sharpe ratio for the portfolio
3.5 Interpret the Sharpe ratio calculated in 3.4

Isabel Myers was a pioneer in the study of personality types. In a random sample of 62
professional actors, it was found that 39 were extroverts.
(a) Let p represent the proportion of all actors who are extroverts, Find the point estimate for p.
(b) Find a 95% confidence interval for the p. Give a brief interpretation of the meaning of the
confidence interval you have found.
(c) Do you think the conditions np greater than 5 and nq greater than 5 are satisfied in this problem? Explain why this
would be an important consideration.

1. A consumer advocacy group suspects that a local supermarket’s 10 ounce packages of cheddar cheese actually weighs less than 10 ounces. The group took a random sample of 20 such packages and found that the mean weight for the sample was 9.955 ounces. The population is normally distributed with a standard deviation of .15 ounces. Test at the .01 level. ( Chap 9 ) (One tailed test)

1. Use the either the p-value approach or the critical value approach to test the hypothesis that Ho; µ = 10 and H1; µ < 10. (Test at the .01 level) Show me your pvalues or zcrit values and state whether you accept or reject the Null Hypothesis.

Test at the .05 level. Show me your pvalues or zcrit values and state whether you accept or reject the Null Hypothesis

For a pair of dice, if the discrete random variable is defined by χ= {█(1 if a=b@max⁡(a,b)if a≠b)┤
(i) Determine the χ; χ(S) (ii) Construct the probability distribution table of χ;f(xi) (iii) Find the expected value χ;E(χ) (v) Variance (vi) Standard deviation (vi) Normal interval for

Hypothesis test for M&Ms:

This section will work through constructing and interpreting a hypothesis test for

proportions. You can find the information for constructing a hypothesis test in

section 10.2. We will be using the p-value approach with a 5% significance level.

1. Treat your bag of M&M’s as a simple random sample. Choose your favorite

color of M&M’s you will be working with for this project. State the color

and give the counts below.

Color of choice: Green

The proportion of M&M's in your color: I had 12 green M&Ms in bag and total of M&Ms = 100... so 12/100?

The hypothesized proportion of M&M’s in your color:?

2. State the null and alternate hypothesis in both symbolic and sentence

form.

3. Use technology to find and state the p-value.

4. Based on your p-value and the significance given above, give the

conclusion of your hypothesis test.

A random sample of n₁ = 283 voters registered in the state of California showed that 140 voted in the last general election. A random sample of n₂ = 217 registered voters in the state of Colorado showed that 129 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p₁ = p₂; H₁: p₁ ≠ p₂H₀: p₁ = p₂; H₁: p₁ > p₂    H₀: p₁ = p₂; H₁: p₁ < p₂H₀: p₁ < p₂; H₁: p₁ = p₂

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. The number of trials is sufficiently large.The Student's t. We assume the population distributions are approximately normal.    The standard normal. We assume the population distributions are approximately normal.The standard normal. The number of trials is sufficiently large.

What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


(d)Sketch the sampling distribution and show the area corresponding to the P-value.

(e) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(f) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.Fail to reject the null hypothesis, there is insufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.    Reject the null hypothesis, there is sufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.Reject the null hypothesis, there is insufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.

Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 95 politically conservative voters, r₁ = 16 responded yes. Another random sample of n₂ = 77 politically moderate voters showed that r₂ = 20 responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use α = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p₁ = p₂; H₁: p₁ > p₂H₀: p₁ < p₂; H₁: p₁ = p₂    H₀: p₁ = p₂; H₁: p₁ < p₂H₀: p₁ = p₂; H₁: p₁ ≠ p₂

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. The number of trials is sufficiently large.The Student's t. We assume the population distributions are approximately normal.    The Student's t. The number of trials is sufficiently large.The standard normal. We assume the population distributions are approximately normal.

What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


(d)Sketch the sampling distribution and show the area corresponding to the P-value.

(e) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

(f) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.Fail to reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.    Reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.Reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters favoring more tax dollars for the arts is less than the proportion of moderate voters.

A random sample of n₁ = 16 communities in western Kansas gave the following information for people under 25 years of age.

x₁: Rate of hay fever per 1000 population for people under 25

A random sample of n₂ = 14 regions in western Kansas gave the following information for people over 50 years old.

x₂: Rate of hay fever per 1000 population for people over 50

(i) Use a calculator to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use α = 0.05.
(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ > μ₂H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂    H₀: μ₁ > μ₂; H₁: μ₁ = μ₂H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.    The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250    0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

d) Sketch the sampling distribution and show the area corresponding to the P-value.

(e) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.    At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(f) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.    Fail to reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.Fail to reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.