A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x₁ be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x₂ be the empathy score of a father. A random sample of 37 mothers gave a sample mean of x₁ = 69.72. Another random sample of 29 fathers gave x₂ = 59.51. Assume that σ₁ = 12.32 and σ₂ = 11.55.

(a) Let μ₁ be the population mean of x₁ and let μ₂ be the population mean of x₂. Find a 95% confidence interval for μ₁ – μ₂. (Use 2 decimal places.)

(b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 95% confidence level?

Because the interval contains only positive numbers, we can say that the mothers have a higher mean empathy score.Because the interval contains both positive and negative numbers, we can not say that the mothers have a higher mean empathy score.    We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that the fathers have a higher mean empathy score.

1. A researcher wants to know if being monolingual, bilingual, or multilingual is related to which country a person is from. To assess this, a large group of people were surveyed. The results of that survey are reported below. Are the traits related? (3 points)

Two manufacturing processes are being compared to try to reduce the number of defective products made. During 8 shifts for each process, the following results were observed:

Based on a 5% significance level, did line B have a larger average than line A?

*Do not use the p-value method

*Use the five step method

Step 1: H₀ :

H_A:

Step 2: alpha =

Step 3: Test Statistic:

Step 4: Decision Rule:

Step 5: Calculation and Decision

Reject or do not reject H₀? Why?

Based on a 5% significance level, did line B have better performance than line A in terms of process variation?

*Do not use the p-value method

*Use and show the five step method, as shown above

Reject or do not reject the H₀? Why?

A power network involves three substations A, B, and C. Overloads at any of these substations might result in a blackout of the entire network. Past history has shown that if substation A alone experiences an overload, then there is a 1% chance of a network blackout. For stations B and C alone these percentages are 2% and 3%, respectively. Overloads at two or more substations simultaneously result in a blackout 5% of the time. During a heat wave there is a 64% chance that substation A will experience an overload, a 24% chance that substation B will experience an overload, and a 19% chance that substation C will experience an overload. There is a 3% chance that exactly two of the substations will simultaneously experience overload, and it is equally likely to be any two of the three. Finally, there is a 2% chance that all three substations experience an overload.

a) What is the probability that a blackout due to an overload occurs during a heat wave?

b) If a blackout occurred during a particular heat wave, what is the probability that the substation A alone experienced an overload?

c) If a blackout occurred during a particular heat wave, what is the probability that an overload occurred at two or more substations simultaneously?

Thank you!

The table below provides several temperature values taken at various altitudes

Altitude(in the thousands of feet) 3 10 14 22 28 31 33

Temperature                           57 37 24 -5 -30 -41 -54

Determine if there is linear correlation between altitude and temperature. Give the appropriate r-value(do not calculate this value by hand) and what values you used to determine if there was or was not correlation. Conduct a hypothesis test at the 0.05 level of significance and List the equation of best fit(found via technology) and use this equation to find the predicted temperature at 6327 feet(show the calculation).

Show ALL WORK in a sample step to step process please

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. In the following data pairs, A represents birth rate and B represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information. A: 11.6 12.4 12.8 13.0 13.4 12.0 14.2 15.1 B: 11.1 12.7 12.7 11.1 13.9 13.1 10.9 10.0 A: 12.5 12.3 13.1 15.8 10.3 12.7 11.1 15.7 B: 14.1 13.6 9.1 10.2 17.9 11.8 7.0 9.2 Do the data indicate a difference (either way) between population average birth rate and death rate in this region? Use α = 0.01. (Let d = A − B.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)

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

X is a continuous uniform (0,8) random variable. Define Y=X^2.

What is the mean square error of the estimate of μY based on 40 independent samples of X?

e_n = ?

Administrative assistants in a local university have been asked to prove their proficiency in the use of spreadsheet software by taking a proficiency test. Historically, the mean test score has been 74 with a standard deviation of 4. A random sample of size 40 is taken from the 100 administrative assistants and asked to complete the proficiency test.

What is the probability that the sample mean score is more than 75, the predetermined passing score?

A marketing research firm wishes to compare the prices charged by two supermarket chains—Miller’s and Albert’s. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores. The stores for each chain are randomly selected, and all purchases are made during a single week. It is found that the mean and the standard deviation of the shopping expenses at the 10 Miller’s stores are x1¯¯¯¯?=?$115.41x1¯?=?$115.41 and s₁= 1.12. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Albert’s stores are x2¯¯¯¯?=?$115.27x2¯?=?$115.27 and s₂= 2.39.

(a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Test statistic          

(b) Calculate the critical value. (Round your answer to 2 decimal places.)

Critical value          

(c) At the 0.05 significance level, what it the conclusion?

Suppose the following data are product weights for the same items produced on two different production lines.

Test for a difference between the product weights for the two lines. Use α = 0.05.

State the null and alternative hypotheses.

H₀: The two populations of product weights are identical.
H_a: The two populations of product weights are not identical.H₀: Median for line 1 − Median for line 2 < 0
H_a: Median for line 1 − Median for line 2 = 0    H₀: The two populations of product weights are not identical.
H_a: The two populations of product weights are identical.H₀: Median for line 1 − Median for line 2 ≤ 0
H_a: Median for line 1 − Median for line 2 > 0H₀: Median for line 1 − Median for line 2 ≥ 0
H_a: Median for line 1 − Median for line 2 < 0

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.    Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

a) By how much does the model estimate the crime rate would change due to a 1% increase in the percentage of students receiving free lunch (assuming all other things are constant)? What about 2.5%?

b) By how much does the model estimate the crime rate would decrease due to a 1,000 person increase in the total population (assuming all other things are constant)?

c) By how much does the model estimate the crime rate would change due to a 5,000 person increase in the total population (assuming all other things are constant)?

d) Use the full model specified above to predict the crime rate for a Denver neighborhood with a total population of 7,000 and 18% of the student population receiving free lunch. (Enter your answer to three decimal places.)

We often judge other people by their faces. It appears that some people judge candidates for elected office by their faces. Psychologists showed headand-shoulders photos of the two main candidates in 32 races for the U.S. Senate to many subjects (dropping subjects who recognized one of the candidates) to see which candidate was rated “more competent” based on nothing but the photos. On election day, the candidates whose faces looked more competent won 22 of the 32 contests.

a) Plot the log-likelihood function for these data in R.

b) Based on your plot, what is the approximate maximum likelihood estimate of the probability that the candidate who appears more competent will win the election?

c) Estimate the 95% confidence interval for your answer to part b.

d) Use the likelihood ratio test or the binomial test to test the null hypothesis that the probability is 0.5. Can you reject this null hypothesis?

Use the dataset “ChickWeight”, available in R. Assume that each row is an observation of a unique chick. weight is the weight of the chick. Diet is the diet treatment that the chick received. Assume that the distribution of chickweigts within each diet is approximately normal and variances are equal.

1. Construct a 95% confidence interval for the true mean weight of chicks.

2. Interpret the confidence interval in 1. in the context of the problem.

3. Construct a 99% confidence interval for the true mean weight of chicks.

4. Interpret the confidence interval in 2. in the context of the problem.

5. Write down the null and alternative hypothesis to determine if the mean weight of chicks is greater than 120.

6. Conduct a statistical test to determine if the mean weight of chicks is greater than 120. Use = 0.05.

7. Construct a box-and-whisker plot of weight by Diet. Label the graph and axes appropriately. (Hint: there should be 4 box-and whisker plots on one graph)

8. Write down the null and alternative hypothesis to determine if there is a difference in mean weight between diets.

9. Use an ANOVA to determine if there is a difference in mean weights between diets. Assume that all of the assumptions are met to perform the procedure. = 0.05.

10. If there is a difference in mean weights between diets, use a statistical procedure to rank the means where possible.

Billy’s Bakery bakes fresh bagels each morning. The daily demand for bagels is a random variable

with a distribution estimated from prior experience given by

The bagels cost Billy’s $0.08 to make, and they are sold for $0.35 each. Bagels unsold at the end

of the day are purchased by a nearby charity soup kitchen for $0.03 each.

a) Simulate the discrete distribution for demand for 100 days, and compare the expected daily profit of Q = 25 and Q = 27.

b) Repeat part a) using a normal distribution with m = 18 and s = 8.86 for demand.

Submit a brief description of how you set up your simulations. This description must explain how you generated the random demands and any formulas that you used.

Consider the following sample data.

(a) Find the mean and standard deviation for each sample.

(b) What does this exercise show about the standard deviation?

____The idea is to illustrate that the standard deviation is not a function of the value of the mean.

____The idea is to illustrate that the standard deviation is a function of the value of the mean.