Low birth weights are considered to be less than 2500 g for newborns. Birth weights are normally distributed with a mean of 3150 g and a standard deviation of 700 g.

a) If a birth weight is randomly selected what is the probability that it is a low birth weight?

b) Find the weights considered to be significantly low using the criterion of a probability of 0.02 or less. That is, find the weight ranked as the lowest 2%.

c) Find the weight ranked as the highest 2%

d) Find the probability of a birth weight between 2600 g and 3500 g.

Can someone please describe the relationship between f-value/ratio, p-value, and alpha value (0.05) in the ANOVA and provide a good example

The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4680 households discard waste with weights having a mean that exceeds 27.22 lb/wk. For many different weeks, it is found that the samples of 4680 households have weights that are normally distributed with a mean of 26.95 lb and a standard deviation of 12.13 lb. What is the proportion of weeks in which the waste disposal facility is overloaded? P(M > 27.22) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. Is this an acceptable level, or should action be taken to correct a problem of an overloaded system? Yes, this is an acceptable level because it is unusual for the system to be overloaded. No, this is not an acceptable level because it is not unusual for the system to be overloaded.m

A new LED light to replace incandescent bulbs has come on the market. The box says it has an average life of 8000 hours with a standard deviation of 200 hours.

A.) What is the probability that a single bulb will last between 7950 and 8100 hours?

B.) What is the probability that the mean of a sample of 75 bulbs picked at random will be between 7950 and 8100 hours?

An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of the nine accounts selected. The number of errors found in each of techniques A and B is listed in the table below:

Select a 90% confidence interval for the true mean difference in the two techniques.

a) [0.261, 8.627]

b) [-4.183, 4.183]

c) [2.195, 6.693]

d) [3.050, 5.838]

e) [2.584, 6.304]

f) None of the above

An experimenter is investigating the effects of noise on the performance of a tracking task. The task is to use a mouse to keep a cursor on a computer screen on a randomly moving target dot. The dependent variable is the amount of time a person can keep the cursor on the dot. It was hypothesized that subjects performing the task when no environmental noise is present will keep the cursor on the target for a greater amount of time than subjects who perform the task while listening to loud noise.

Each action by the experimenter that is described next confounds this experiment by letting an extraneous variable vary systematically with the independent variable of noise condition. For each action, identify the extraneous variable confounding the experiment and explain why the experiment is confounded.                                                                                            

Perform a three way t-test on the following data: 5.31 +/- 2.32 (n=3), 1.89 +/- 0.368 (n=3), and 8.08 +/- 0.0495 (n=2).

A social psychologist is designing a study to see whether people who see a particular film will be more likely to see violence as a solution to a problem. The psychologist plans to use a scale that assesses this construct, the Problem-Violence Scale, which has a population mean of 85, a standard deviation of 10, and is normally distributed. The psychologist takes a sample of 20 people, randomly and shows them the film prior to having them solve problems. On the Problem-Violence Scale mentioned, this sample scores a mean of 88. The research question is, does the film cause an increase in the use of violence to solve a problem? Use a one-tailed test with a significance level of .05 to conduct the steps of hypothesis testing. What is the Research & Null hypothesis? Determine the characteristics of the comparison distribution to compare to sample distribution:

Match these non-parametric statistical tests with their parametric counterpart by putting the corresponding letter on the line.

_____ Friedman test

_____ Kruskal-Wallis H test

_____ Mann-Whitney U test

_____ Wilcoxon Signed-Ranks t test

A: Paired-sample t-test

B: Independent-sample t-test

C: One-way ANOVA, independent samples

D: One-way ANOVA, repeated measures

1. A researcher suggests that male nurses earn more than female nurses. A survey of 16 male nurses and 20 female nurses reported the following data. Is there enough evidence to support the claim that male nurses earn more than female nurses? Use α=0.05. (4 points)

Female:   = $23,750

                S₁² = $250

                n₁ = 20

Male:        = $23,800

                S₂² = $300

                n₂ = 16

2. Create a 90% confidence interval for the difference between Male and Female salaries. ​

How to use TI-84 to solve, Consider the probability distribution of a random variable X shown below:
f(x) = \binom13x 0.25^x 0.75^13−x,   x = 0,1,2,…13.

What are the mean (μ) and variance (σ²) of the random variable X?
μ = 2.9, and σ² = 2.4375.
μ = 3.25, and σ² = 2.4375.
μ = 2.9, and σ² = 2.9.
μ = 3.25, and σ² = 2.9.

Find the probability:   P(X < 7)?
.

11.7. Machine speed. The number of defective items produced by a machine (Y) is known to be linearly related to the speed setting of the machine (X). The data below were collected from recent quality control records. #d. Estimate the variance function by regressing the squared residuals against-X, and then calculate the estimated weight for each case using (11.16b). #e. Using the estimated weights, obtain the weighted least squares estimates of f30 and th. Are the weighted least squares estimates similar to the ones obtained with ordinary least squares in part (a)? #f. Compare the estimated standard deviations of the weighted least squares estimates bwo and bW1 in part (e) with those for the ordinary least squares estimates in part (a). What do you find? #g. Iterate the steps in parts (d) and (e) one more time. Is there a substantial change in the estimated regression coefficients? If so, what should you do?

   28.0 200.0
   75.0 400.0
   37.0 300.0
   53.0 400.0
   22.0 200.0
   58.0 300.0
   40.0 300.0
   96.0 400.0
   46.0 200.0
   52.0 400.0
   30.0 200.0
   69.0 300.0

Show, organize, and label (SOL) your work. Use correct notation as done in class or the book. If you use a calculator function to do a calculation, write down the keys used. You do not have to write down calculator steps if you’re just using a calculator to do arithmetic calculations.

1. At the Shenandoah Valley Produce Auction (SVPA) a box contains 5 ghost pumpkins with the following weights: {5 lbs, 7 lbs, 8 lbs, 11 lbs, 14 lbs}. Let X = weight of ghost pumpkins in the box.

a) Fill in the missing cells in the table below. Calculate the mean and standard deviation for all 3 columns. Note: You should use the population standard deviation formula.

b) How did transforming the original data (X) by subtracting the mean of the original data change the mean? In other words, what is the mean of Y? How did dividing by the standard deviation change the standard deviation of the original data? In other words, what is the standard deviation of Z?

c) Does the variable Z have a standard normal distribution? Why did you answer the way you did? Think about what properties a standard normal distribution has.

d) What is the probability that X is greater than 7 if a pumpkin is randomly chosen from the box (should be very simple to answer)? How does this compare to the probability that the weight of a randomly chosen pumpkin has a Z-score greater than the z-score of 7 (again easy to answer)?

2.. The SVPA sells a box of 6 Blue Hubbard pumpkins. The mean weight of all the pumpkins in the box is 14.5 lbs. The table below shows the distribution of the sample mean weight if 3 pumpkins are selected randomly from the box.

a. Suppose the three pumpkins selected are 3lbs, 9 lbs and 21 lbs. Construct a 60% confidence interval on the population mean using this sample. Explain how you figured out the margin of error.

b. Interpret the 60% confidence interval found in part a. Give the full interpretation and use the context of the problem

c. The SVPA claims that based on years of data the mean weight of the pumpkins in the box is 14.5 lbs. Does the 60% confidence interval from part a contradict this claim?

d. What is the probability the mean weight of the pumpkins in the box is in the 60% confidence interval found in part a. Explain.

e. For the hypotheses H₀: μ = 14.5 lbs and H₁: μ ≠ 14.5 lbs on the mean weight of the pumpkins in the box, what would the p-value be for the hypothesis test using the sample from part a. Use correct notation. Explain what the p-value represents within the context of the problem.

f. For the hypothesis test in part e, what would be the lowest significance level at which we would reject the null hypothesis? Explain.

3. Giant pumpkins frequently don’t contain seeds when cut open because of excessive in-breeding. This is unfortunate since seeds can sell for $30 each or more. In a sample of 50 giant pumpkins, 23 did not contain seeds.

a) What is the point estimate for the proportion of giant pumpkins that don’t have seeds?

b) Show that the necessary conditions are satisfied for the sample proportion to have an approximately normal distribution.

c) Using the sample above an obstreperous giant pumpkin researcher wants to use the unusual confidence level of 75% to create a confidence interval for the true proportion of giant pumpkins not containing seeds

                i) What would be the standard error for the sample proportion? Use p-hat as an estimate of p.

                ii) What is the critical value for this confidence interval?

                iii) What is the margin of error?

                iv) What is the75% confidence interval?

d) Interpret the 75% confidence interval within the context of the problem.

e) What sample size would be necessary to produce a margin of error equal to 5 percentage points assuming the true proportion is equal to the sample proportion from above?

Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been taken from two normally distributed populations having variances σ12 and σ22 give sample variances of s12 = 94 and s22 = 13. (a) Test H0: σ12 = σ22 versus Ha: σ12 ≠ σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = 7.231 F.025 = H0:σ12 = σ22 (b) Test H0: σ12 < σ22versus Ha: σ12 > σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = 4.147 F.05 = H0: σ12 < σ22