What is First Order Autocorrelation and what effect does it have on the Least Squared Estimates of Linear regression model?

The sample of 10 healthy children has an average serum iron level 19휇mol/l with a standard deviation 6휇mol/l. The sample of 6children with cystic fibrosis has an average iron level 12휇mol/l with a standard deviation of 6.3. An investigator wants to test whether the mean serum iron levels differ between children with and without cystic fibrosis at 95% confidence level(two-sided). Assume that the serum iron level is approximately normally distributed.

a)State the null and alternative hypotheses.

b)Calculate the pooled estimate of the variance.

c)Which test statistic do we need to use? t or z? Why?

d)Calculate an appropriate test statistic.

e)Calculate a p-value.

f)Can you reject H0at 95% confidence level?

g)Interpret the result.

Janet was asked the following question on her Probability Test:    Q: A class has 7 boys and 6 girls. The teacher will be picking two volunteers at random to do the recycling. What is the probability that the teacher picks one boy and one girl?

Janet's answer along with her explanation is shown below:

Well there is a 7/13 chance of picking a boy and a 6/13 chance of picking a girl- therefore, the probability of picking a boy AND a girl will be P(Boy) x P(Girl) = 7/13x6/13=42/169=25%.

Explain , in detail if you agree with her answer. Include in your answer references to independent and dependent events. If you agree that her answer is correct, explain why. If you disagree with her answers, explain what she did wrong and include the correct solution.

A variable is normally distributed with mean 15 and standard deviation 4.

a. Find the percentage of all possible values of the variable that lie between 8 and 19.

b. Find the percentage of all possible values of the variable that are at least 12.

c. Find the percentage of all possible values of the variable that are at most 13.

Among a sample of 16 people, the average heart rate was 69.0 beats per minute with a standard deviation 4.3 beats per minute. We are interested in the mean heart rate of the population. We assume that the heart rate is normally distributed, and that the population standard deviation is 4.8 beats per minute. At 95% confidence, what is the error bound?

Determine the value of the coefficient of correlation, r, for the following data.

(Round the intermediate values to 3 decimal places. Round your answer to 3 decimal places.)


r =

Chapter 8. A sample of 36 patients in a doctor's office showed that they had to wait an average of 45 minutes with a standard deviation of 12 minutes before they could see the doctor.

Please provide a 95% confidence interval estimate for the average waiting time of all the patients who visit this doctor, and interpret your results (write a sentence explaining the results).

M/PF Research, Inc. lists the average monthly apartment rent in some of the most expensive apartment rental locations in the United States. According to their report, the average cost of renting an apartment in Minneapolis is $951. Suppose that the standard deviation of the cost of renting an apartment in Minneapolis is $96 and that apartment rents in Minneapolis are normally distributed. If a Minneapolis apartment is randomly selected, what is the probability that the price is:

(Round the values of z to 2 decimal places. Round answers to 4 decimal places.)

(a) $1,010 or more?

(b) Between $880 and $1,120?

(c) Between $825 and $935?

(d) Less than $730?

CALCULATING PROBABILITIES USING TREE DIAGRAMS AND COMBINATIONS

Two apples are chosen from a basket containing five red and three yellow apples. Draw a tree diagram below, and find the following probabilities.

1) P(one red, one yellow)

2) P(First red and second yellow)

Three marbles are drawn from a jar containing five red, four white, and three blue marbles. Find the following probabilities using combinations.

1) P(two white and 1 blue)

2) P(at least one red)

A committee of four is selected from a total of 4 freshmen, 5 sophomores, and 6 juniors. Find the probabilities for the following events.

1) No sophomores.

2) Not all four from the same class.

3) More juniors than freshmen and sophomores combined.

1. A researcher is interested in whether college students get enough sleep. She suspects that they get less than 8 hours of sleep on average. The sample mean (x¯) for 65 students was 7.08 hours. The standard deviation of number of hours students slept is s=1.8.

(a) Determine the null and alternative hypothesis for the test. What is the parameter in this study?

(b) The p-value for the test is <0.0001. Using a significance level of .05, write a one or two sentence conclusion in context of the problem.

(c) Calculate 95% confidence interval for µ, the mean number of hours college students sleep per night. Interpret the confidence interval. Be sure to use the word mean or average in your interpretation and don’t forget units. If you are doing the calculations by hand use t∗ = 1.998.

(d) Does your confidence interval support the results of the hypothesis test? Explain.

Describe a confidence interval for the mean of a population by stating 1. a population and a quantitative variable on that population, 2. a sample size, 3. a sample mean of that variable, and 4. a sample standard deviation, and 5. a confidence level, then 6. finding the interval. Then perform a test of significance on the mean of the population by stating 7. both a null and an alternative hypothesis and 8. an α-level, then finding 9. the one-sample t-statistic and either 10. rejecting or failing to reject the null hypothesis. Remember that you do not need to list the values of the variable for individuals in either the sample or the population, and that the values for 2, 3, 4, 5, and 8 do not need to be calculated, only stated.

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

Production Volume (units) Total Cost ($)

400 4,900

450 5,900

550 6,300

600 6,800

700 7,300

750 7,900

Compute b1 and b0 (to 1 decimal). b1 b0 Complete the estimated regression equation (to 1 decimal). ŷ = + x

What is the variable cost per unit produced (to 1 decimal)?

Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1. r2 =

What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)? %

The company's production schedule shows 500 units must be produced next month.

What is the estimated total cost for this operation (to the nearest whole number)? $

A simple random sample with

n = 55

provided a sample mean of 24.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.)

A. Develop a 90% confidence interval for the population mean.

B. Develop a 95% confidence interval for the population mean.

C. Develop a 99% confidence interval for the population mean.

Refer to the accompanying data set and construct a 95% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.

Males   Females
84   81
72   97
51   56
62   67
55   54
64   81
51   78
79   87
53   86
63   56
71   37
59   67
63   84
81   77
85   78
64   61
65   67
96   81
45   58
89   65
69   85
64   81
71   70
70   75
54   86
64   92
53   89
78   93
70   89
65   91
64   69
98   91
58   80
69   82
59   76
59   54
71   98
68   77
85   75
60   77

Discuss the following processes/issues regarding qualitative data analysis:

Preliminary processes to analysis and the manner in which they best enhance qualitative data analysis.