1- The number of calories in a hamburger depends on what ingredients are included. The following are determinations of calorific values of a sample of homemade large hamburgers:

350 375 400 356 378 379 340 320 330 324 360 390

Assume that the calorific values for the hamburgers are normally distributed.

a) Find the standard error of the sample mean.

b) Obtain the 95% confidence intervals for the mean calorific values of the burgers.

2- The following show the number of hours a sample of High school students from a local high school studied a week:

21, 15, 18, 24, 15, 18, 20, 23, 24, 12, 10, 20, 12, 18, 20, 14, 17

Assume that the weekly study hours are normally distributed.

a) find the 90% confidence intervals for the mean number of study hours.

b) find the margin of error for the 95% confidence interval of the mean number of study hours for all students in this high school. The margin of error equals half length of the confidence interval.

The joint pmf of ? and ? is given by ??,? (?, ?) = (? + ?)/ 27 ??? ? = 0, 1,2; ? = 1, 2, 3, and ??,? (?, ?) = 0 otherwise. a. Find ?(?|? = ?) for all ? = 0,1, 2. b. Find ?(3 + 0.2?|? = 2).

(Please solve manually.)  Every April Americans and Canadians fill out their tax return forms. Many turn to tax preparation companies to do this tedious job. The question arises, Are there differences between companies? In an experiment two of the largest companies were asked to prepare the tax returns of a sample of 55 taxpayers. The amounts of tax payable were recorded. Can we conclude that company 1’s service results in higher tax payable?

Folder on Blackboard contains information on the hourly wages in pounds of a sample of young Scottish workers aged 20-24.Use these data to answer the following nine questions.

For numerical questions provide your answer to four decimal places.

1. Calculate the mean wage in the sample in pounds.

2. Calculate the sample standard deviation of the wage in pounds.

(Assuming that I have the right answers for the above two questions which I have from an excel sheet, how do I proceed after I calculated the above two questions answers, like what formulas do I use)

Questions 3-6 use the following information. It is claimed that the “Living Wage” for workers at the time this sample was taken was £7.80. You are asked to test whether the average wage of young workers aged 20-24 is less than the Living Wage.

3. What are the null and alternative hypotheses?

4. What is the value of the test statistic for conducting this test?

5. To do a test at the 2% level of significance what critical value would you use?

6. What would be the conclusion of your test?

7. Calculate the proportion of workers in the sample earning below the Living Wage.

8. Calculate the standard error of this sample proportion of workers.

Question 9 requires the following information. A Scottish government minister claims that the proportion of young Scottish workers earning below the Living Wage is 60%. You are asked to test if the sample proportion of young workers aged 20-24 is below this figure.

9. What is the value of the test statistic for conducting this test?

1. The data below show the volume of transactions​ (in hundreds of​ thousands) in shares of a corporation over a period of 12 weeks. Using these​ data, estimate a​ first-order autoregressive​ model, and use the fitted model to obtain forecasts of volume for the next 3 weeks.

Week   Trading Volume
1   27.8
2   14.6
3   14.4
4   13.8
5   23.4
6   17.8
7   7.2
8   25.3
9   21.8
10   17.2
11   26.5
12   21.5

The estimated​ first-order autoregressive model is x^{^}_t = (?) + (?)x_t-1

The following data were collected in an experiment designed to investigate the impact of different positions of the mother during ultrasound on fetal heart rate. Fetal heart rate is measured by ultrasound in beats per minute. The study includes 20 women who are assigned to one position and have the fetal heart rate measured in that position. Each woman is between 28-32 weeks gestation. The data are shown below.

Is there a significant difference in mean fetal heart rates by position? Run the test at a 5% level of significance.

The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 30. A pollster draws a sample of 92 people to interview.

A) What is the probability that the sample mean income is less than 37? Round the answer to at least four decimal places.

B) What is the probability that the sample mean income is between 40 and 44? Round the answer to at least four decimal places.

C) Find the 70^th percentile of the sample mean. Round the answer to at least one decimal place.

D) Would it be unusual for the sample mean to be less than 37? Round the answer to at least four decimal places.

E) Do you think it would be unusual for an individual to have an income of less than 37? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.

1. The General Social Survey (2008) asked a random sample of people whether they agree with the following statement: A husband’s job is to earn money; a wife’s job is to take care of the home. Based on this data (displayed below), conduct a chi-square hypothesis test to assess whether there are statistically significant gender differences in feelings about gender roles ( = 0.05). Male Female Total Agree 183 192 375 Neither 143 140 283 Disagree 288 412 700 Total 614 744 1,358 a. Write out the hypotheses (2 points). b. Calculate degrees of freedom (1 point). c. Construct a table of expected frequencies (fe) (6 points). d. Compute the chi-square statistic. Create a table like the ones we used in class to help you (11 points). e. Determine the p-value (1 point). f. Decide whether there is evidence to reject the null hypothesis (use = 0.05). Justify your decision (2 points). g. Interpret the results of the hypothesis test in terms of the wording of the problem (2 points).

The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 207.50 cm. b. Find the probability that the mean for 25 randomly selected distances is greater than 193.20 cm. c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30? a. The probability is _______

I need clear steps / formulas used with (F) ( I'm lost with current solutions )

To get full marks for the following questions you need to convert the question from words to a mathematical expression (i.e. use mathematical notation), defining your random variables where necessary, and using correct probability statements. Suppose that the IQ of adults is normally distributed with a mean of 100 and standard deviation of 15. (a) [2 marks] What IQ score distinguishes the highest 10%? (b) [3 marks] What is the probability that a randomly selected person has an IQ score between 91 and 118? (c) [2 marks] Suppose people with IQ scores above 125 are eligible to join a high-IQ club. Show that approximately 4.78% of people have an IQ score high enough to be admitted to this particular club. (d) [4 marks] Let X be the number of people in a random sample of 25 who have an IQ score high enough to join the high-IQ club. What probability distribution does X follow? Justify your answer. (e) [2 marks] Using the probability distribution from part (d), find the probability that at least 2 people in the random sample of 25 have IQ scores high enough to join the high-IQ club. (f) [3 marks] Let L be the amount of time (in minutes) it takes a randomly selected applicant to complete an IQ test. Suppose L follows a uniform distribution from 30 to 60. What is the probability that the applicant will finish the test in less than 45 minutes?

Find the ‘best fit’ equation of net income for last year on last year’s sales. Test the significance of the overall model at 1% level of significance.

Find the ‘best fit’ equation of net income for last year on last year’s sales. Test the significance of the overall model at 1% level of significance.

In a test given to two groups of students to marks were as follows:

First group: 9, 11, 13, 11, 15, 9, 12, 14

Second group: 10, 12, 10, 14, 9, 8, 10

Examine the significance of difference μ1-μ2 under the assumption on the samples are drawn from normal population with σ12=σ22.

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.)