two randomly assigned groups are compared in a health pilot evaluation project. data down on both groups are assumed to be normally distributed. the mean for the group 1 is 280, with a standard deviation of 15. the mean for group 2 is 230, with a standard deviation of 8. the number of observation for each group is 45. assume the level of significance is 5%. determine whether these two groups are statistically similar. show your hypothesis, calculated and critical t-values, decision and conclusion.

1. What is a p-value and how is it used to make a decision about the null hypothesis?
2. How is the p-value related to the test statistic?
3. Explain whether or not rejecting the null hypothesis makes the alternative hypothesis true and why.
4. If I conduct a hypothesis testing with Type I error set at 0.05 and a resulting p-value of 0.3, what would my conclusion be?

3.)

A professional employee in a large corporation receives an average of μ = 39.8 e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 38 employees showed that they were receiving an average of x = 33.1 e-mails per day. The computer server through which the e-mails are routed showed that σ = 16.2. Has the new policy had any effect? Use a 10% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. Are the data statistically significant at level α? Based on your answers, will you reject or fail to reject the null hypothesis?

Select one:

a. The P-value is greater than than the level of significance and so the data are not statistically significant. Thus, we fail to reject the null hypothesis.

b. The P-value is less than than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.

c. The P-value is less than than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.

d. The P-value is less than than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis.

e. The P-value is less than than the level of significance and so the data are not statistically significant. Thus, we fail to reject the null hypothesis.

Here is a random sample of the body temperature of 25 young adults.

96	96.6	96.7	96.9	97
97.1	97.1	97.2	97.3	97.4
97.4	97.7	97.7	97.7	97.8
97.9	98	98	98.2	98.2
98.3	98.3	98.7	98.8	98.9

Complete the relative frequency distribution table.

Temperature Group	Frequency	Relative Frequency	Cumulative
96 ≤ x < 96.41	1	1/25
96.41 ≤ x < 96.82	2	2/25
96.82 ≤ x < 97.23	5	5/25
97.23 ≤ x < 97.64	3	3/25
97.64 ≤ x < 98.05	7	7/25
98.05 ≤ x < 98.46	4	4/25
98.46 ≤ x < 98.87	2	2/25
98.87 ≤ x < 99.28	1	1/25

Data are collected on the relationship between the number of hours per week practicing a musical instrument and scores on a math test. The line of best fit is as follows: ŷ = 72.5 + 2.8x.

What would you predict the score on a math test would be for a student who practices a musical instrument for 1.2 hours a week? Round to one decimal place.

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (sigma1 = sigma2), so that the standard error of the difference between means is obtained by pooling the sample variances. A paint manufacturer wanted to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Construct a 99% confidence interval for mu1 - mu2, the difference between the mean drying time for paint type A and the mean drying time for paint type B.

An advertisement for A-1 Motor Oil states that in a survey of auto mechanics across the country, the majority of them use A-1 Motor Oil in their own vehicles.

a. correlation does not imply causality b. voluntary response survey c. self-interest survey d. poorly worded questions

In Nebraska, the average ACT score is 21.7 with a standard deviation of 1.1. We collect a random sample of 30 students who took the exam last year.

Part 1: (6 pts)

Check the all necessary conditions in detail (not just yes or no) (1 pt each) and give the sampling model and parameters to 2 decimal places (2 pts).

Part 2: (8 pts)

What is the probability that the average composite ACT score is 22.1 or more? Show your calculations for finding the z-score to three decimal places (4 pts), then find the probability to four decimal places using the appropriate probability notation (2 pts). Write a sentence that gives your solution in context (2 pts).

1. Two companies market new batteries targeted at owners of personal music players. Dura Tunes claims a mean battery life of 11 hours, while RockReady advertises 12 hours.

a. Explain why you would also like to know the standard deviations of the battery lifespans before deciding which brand to buy.

b. Suppose the standard deviations are 2 hours for DuraTunes and 1.5 hours for RockReady. You are headed for 8 hours at the beach. Which battery is most likely to last all day? Explain.

PLEASE SHOW ALL WORK AND RATIONALE.

TYPED WORK ONLY PLEASE

NO HANDWRITTEN.

Eight samples (m=8) have been collected from a manufacturing process that is in statistical control, and the dimension of interest has been measured for each part. It is desired to determine the values of the center, LCL, and UCL for ?̅ and R charts. The calculated ?̅ values (units are in mm) are 2.723, 1.993, 2.008, 1.723, 1.999, 2.001, 1.995 and 2.723 The calculated R values (mm) are 0.015, 0.021, 0.020, 0.023, 0.723, 0.723, 0.014 and 0.011. Also plot the control chart. Comment on your answer.

​ 62% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is ​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

1) A population of values has a normal distribution with μ = 97.3 and σ = 21.5 .

You intend to draw a random sample of size n = 42 .

A) Find the probability that a single randomly selected value is greater than 107.3. P(X > 107.3) =

Round to 4 decimal places.

B) Find the probability that the sample mean is greater than 107.3. P( ¯¯¯ X > 107.3) =

Round to 4 decimal places.

Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

2) Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 11.3 years and a standard deviation of 1 years.

A) Find the probability that a randomly selected quartz time piece will have a replacement time less than 8.7 years? P(X < 8.7 years) = Enter your answer accurate to 4 decimal places.

Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

B) If the company wants to provide a warranty so that only 1.5% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?

warranty = years Enter your answer as a number accurate to 1 decimal place.

Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A manufacturing process has two assembly lines, A and B. Suppose that line A produces 60% of the product. and line B produces the rest. We are told that 5% of the products produced by line A are defective in some way, and 8% of the line B products are defective. it may be helpful to construct a tree diagram with first and second-generation branches to answer the following:

C) if the end product is defective, what is the probability that it was produced by line B

Census data for a city indicate that 64.4​% of the​ under-18 population is​ white, 14.5​% black, 19.5​% Latino, 1.4% ​Asian, and 0.2​% other ethnicities. The city points out that of 25,0092 police​ officers, 64.8​% are​ white, 14.5​% ​black, 19.1​% ​Latino, and 1.4​% Asian. Do the police officers reflect the ethnic composition of the​ city's youth? Test an appropriate hypothesis and state your conclusion.​ (Assume a significance level of alphaαequals=0.05​)

A) Compute the chi-square statistic

B) Compute the P-Value

The Gallup-Healthways Well-being Index is a comprehensive survey of the health status of Americans.  A random sample of 2,580 adults were asked, "Have you ever been told by a physician or a nurse that you have depression?" Of these, 238 answered "Yes."

Using JMP construct the 99% confidence interval for the true proportion of Americans who have been told they have depression, and fill in the appropriate bounds in the confidence interval interpretation given below. Round your answers to two decimal places (i.e. 0._ _).

99% confident the true proportion of Americans who have been told by a physician or nurse they suffer from depression is between

and

Question 2 (1 point)

Refer to the scenario given in Question 1. According to the National Institute of Mental Health, 6.7% of adults suffer from depression. Is this percentage supported by the confidence interval found in Question1?

Question 2 options:

	Yes, because 6.7% does not fall in the confidence interval.
	There is not enough information given to make a determination.
	No, because 6.7% does not fall in the confidence interval.

Question 3 (1.5 points)

Question 3 options:

A study investigated ways to prevent staph infection in surgery patients. In a first step, researchers examined the nasal secretions of a random sample of 6,771 patients admited to various hospitals for surgery. They found that 1,251 of these patients tested positive for Staphylococcus aureus, a bacterium responsible for most staph infections.

Using JMP, find the 90% confidence interval for the true prorportion of patients admitted for surgery that tested positive for Staphylococcus aureus, and fill in the apporpriate bounds in the confidence interval interpretation given below. Round your answers to two decimal places (i.e. 0._ _).

90% confident the true proportion of patients admitted for surgery that tested positive for Staphylococcus aureus is between

and

Question 4 (1 point)

Saved

Refer to the scenario given in Question 3. Suppose a hospital does not have to implement any measures to control for staph infections if the percentage of patients who test positive for Staphylococcus aureus is less than 18%. Based on the confidence interval constructed in Question 3, does the hospital have to worry about controlling for staph infections?

Question 4 options:

	Yes, because the entire confidence interval is not below 18%.
	Yes, because 18% is in the confidence interval.
	There is not enough information to make a determination.