We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data426.dat) (see below) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.

(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

Wages = _________ + __________ LOS

t = _________

P = _________

(c) State carefully what the slope tells you about the relationship between wages and length of service. This answer has not been graded yet.

(d) Give a 95% confidence interval for the slope.

(______ , _______)

worker  wages   los     size
1       55.0977 28      Large
2       60.3942 54      Small
3       55.5375 35      Small
4       48.6244 27      Small
5       56.5636 188     Large
6       38.237  156     Small
7       43.5632 30      Large
8       42.7156 61      Large
9       39.143  65      Large
10      46.1205 23      Small
11      49.5348 68      Large
12      63.0939 76      Small
13      37.3613 57      Small
14      86.4907 44      Large
15      62.1521 103     Large
16      49.2244 51      Large
17      61.2332 63      Large
18      38.775  14      Small
19      47.1923 127     Large
20      38.5997 39      Large
21      38.8533 105     Large
22      46.0433 164     Small
23      64.581  70      Large
24      41.4075 17      Small
25      55.9129 143     Large
26      47.352  107     Small
27      43.1829 22      Small
28      51.886  197     Large
29      51.3497 46      Large
30      60.591  40      Large
31      55.6434 77      Small
32      37.9994 34      Large
33      50.3993 85      Large
34      39.2409 88      Small
35      51.1068 118     Large
36      44.8436 58      Large
37      39.4066 78      Large
38      64.675  47      Small
39      59.4471 142     Large
40      70.2038 93      Small
41      47.4302 168     Small
42      44.8665 33      Small
43      39.4258 27      Large
44      71.8007 69      Small
45      38.5246 46      Large
46      71.9274 68      Small
47      51.5816 22      Large
48      65.4135 18      Large
49      64.9034 76      Small
50      73.0817 97      Large
51      45.4468 35      Large
52      44.2239 56      Large
53      68.4574 87      Large
54      37.7713 60      Small
55      46.0706 86      Small
56      45.3591 62      Large
57      53.7606 21      Small
58      104.9657        74      Large
59      40.4731 71      Small
60      60.6301 97      Large

My Question: How do you run the appropriate chi square test on this data in SPSS? I need to know how to set it up in SPSS and the step by step procedures. What goes in the data view/variable view and how do I run the test?

Which of the following statements about the general exponential equation y = 600 (1.05)t is true? (Assume t is time in years, with t = 0 in 1950.) Check all that apply.

A)After 1950, each year the y-value is 1.05 times greater than the previous year.

B)The initial amount of 600 is increasing at a rate of 1.05% each year after 1950.

C)When t = 1, y is 105% of its original value, 600.

D)The initial amount of 600 is increasing at a rate of 5% each year after 1950.

First National Bank employs three real estate appraisers whose job is to establish a property’s market value before the bank offers a mortgage to a prospective buyer. It is imperative that each appraiser values a property with no bias. Suppose First National Bank wishes to check the consistency of the recent values that its appraisers have established. The bank asked the three appraisers to value (in $1,000s) three different types of homes: a cape, a colonial, and a ranch. The results are shown in the accompanying table. (You may find it useful to reference the q table.)

Consider a refinery that produces three types of motor oil: Standard, Ex- tra, and Super. The selling prices are $9.00, $13.00, and $19.00 per barrel respectively. These oils can be made from three basic ingredients; crude oil, paraffin, and filler. The costs of the ingredients are $19.00, $9.00 and $11.00 per barrel, respectively. Company engineers have developed the following specifications for each oil Standard-60% paraffin, 40% filler Extra-at least 25% crude oil and no more than 45% paraffin Super-at least 50% crude oil and no more than 25% paraffin The CO2 emissions of Standard, Extra, and Super oils are 13.0, 11.8, and 8.0 units per barrel. With a supply capacity of 110, 90, and 70 thou- sand barrels per week for crude oil, paraffin, and filler, what should be blended in order to maximize profits as well as satisfy the requirements of the EPA to minimize the CO2 emissions from all the products of this industry? Solve the problem using the goal programming approach, if th goals are to have a profit greater than or equal to $5 per barrel and CO2 emissions less than or eaual to 10 units per barrel

How does lowering the screening cutoff point effect sensitivity and specificity, Positive predictive value, and Negative Predictive Value of the test assuming prevalence stays the same? Why?

You are a researcher who wants to know if there is a relationship between variable Y and variable X. You hypothesize that there will be a strong positive relationship between variable Y GPA and Variable X hours of sleep. After one semester, you select five students at random out of 200 students who have taken a survey and found that they do not get more than 5 hours of sleep per night. You select five more students at random from the same survey that indicates students getting at least seven hours of sleep per night. You want to see if there is a relationship between GPA and hours of sleep. Using a Pearson Product Correlation Coefficient statistic, determine the strength and direction of the relationship and determine if you can reject or fail to reject the HO:

Variable Y        Variable X    

2.5                      5               

3.4                      8                

2.0                      4               

2.3                     4.5              

1.6                     3     

3.2                     6

2.8                     7

3.5                     7.5

4.0                     6.5

3.8                     7

Heights of 10 year olds. Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. Round all answers to two decimal places.

1. What is the probability that a randomly chosen 10 year old is shorter than 48 inches?

2. What is the probability that a randomly chosen 10 year old is between 50 and 51 inches?

3. If the shortest 10% of the class is considered very tall, what is the height cutoff for very tall? inches

4. What is the height of a 10 year old who is at the 34 th percentile? inches

Using a random sample of n = 50, the sample mean is = 13.5. Suppose that the population standard deviation is σ=2.5.

Is the above statistical evidence sufficient to make the following claim μ ≠15:

?o: μ=15

??: μ ≠15

α = 0.05.

p value = 0

Interpret the results using the p value test.

Reject Ho

or

Do not reject Ho

Most married couples have two or three personality preferences in common. A random sample of 375 married couples found that 134 had three preferences in common. Another random sample of 573 couples showed that 215 had two personality preferences in common. Let p₁ be the population proportion of all married couples who have three personality preferences in common. Let p₂ be the population proportion of all married couples who have two personality preferences in common.

(a) Find a 90% confidence interval for p₁ – p₂. (Round your answers to three decimal places.)

Crimini mushrooms are more common than white mushrooms, and they contain a high amount of copper, which is an essential element according to the U.S. Food and Drug Administration. A study was conducted to determine whether the weight of a mushroom is linearly related to the amount of copper it contains. A random sample of crimini mushrooms was obtained, and the weight (x, in grams) and the total copper content (y, in mg) was measured for each. You may assume that all of the assumptions for regression are valid. Please include three decimal places in all answers.The work for all of the parts will be submitted at the end of the question. The summry data is given below:

n = 30 S_XX = 137.48 S_YY = 5.778 S_XY = 21.29 MSE = 0.0885 x̄ = 15.993

The line is

ŷ = -1.204 + 0.155 x

a) Find a 95% confidence interval for the true mean copper concentration when the weight of the mushroom is 18.2 g.

b)Find a 95% prediction interval for the true copper concentration when the weight of the mushroom is 18.2 g.

c) A value of 18.2 g is the size of an average Crimini mushroom. Is there any evidence to suggest that the you will get 1.9 mg of copper (the amount that is in one bar of dark chocolate) when you eat one average Crimini mushroom? Be sure to mention which interval, from above.

Ten observations were selected from each of 3 populations and an analysis of variance was performed on the data. The following are the results:

A. Using alpha= .05, test to see if there is a significant difference among the means of the three populations.

B. If in part A you concluded that at least one mean is different from the others, determine which mean is different using LSD method. The three samples are (mean) X1=24.8, X2=23.4, X3=27.4.

According to a study conducted for Gateway Computers, 59% of men and 70% of women say that weight is an extremely/very important factor in purchasing a laptop computer. Suppose this survey was conducted using 374 men and 481 women. Do these data show enough evidence to declare that a significantly higher proportion of women than men believe that weight is an extremely/very important factor in purchasing a laptop computer? Use alpha= 0.05.

Write the correct R commands for solving this problem. What is the p value? What is the statistical decision?

Use R command to construct a 90% confidence interval to estimate the difference in proportion of women and men believe that weight is an extremely/very important factor in purchasing a laptop computer.

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester.

In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 36 expectant mothers have mean weight increase of 16.1 pounds in the second trimester, with a standard deviation of 6.1 pounds.

A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds.

Find the $p$-value for the hypothesis test.

The $p$-value should be rounded to 4 decimal places.

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 495 eggs in group I boxes, of which a field count showed about 268 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 784 eggs in group II boxes, of which a field count showed about 272 hatched.

(a) Find a point estimate p̂₁ for p₁, the proportion of eggs that hatch in group I nest box placements. (Round your answer to three decimal places.)
p̂₁ =  

Find a 95% confidence interval for p₁. (Round your answers to three decimal places.)

(b) Find a point estimate p̂₂ for p₂, the proportion of eggs that hatch in group II nest box placements. (Round your answer to three decimal places.)
p̂₂ =  

Find a 95% confidence interval for p₂. (Round your answers to three decimal places.)

(c) Find a 95% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)