What is the normal curve and why is it so important to the world of inferential statistics?

You are a nurse working in a distress center and would like to study the self-esteem of domestic violence victims. You would like to know if self-esteem is associated with education level. You know from the existing literature that self-esteem scores are generally normally distributed with homogeneous variance across education groups. The table below shows the data that you collected for a random sample of clients that recently visited your center. Let the probability of committing a type I error be 0.05. Can you conclude that there is a difference in self-esteem across the education groups? If an overall significant difference is found, which pairs of individual sample means are significant different?

A nursing professor was curious as to whether the students in a very large class

she was teaching who turned in their tests first scored differently from the overall

mean on the test. The overall mean score on the test was 75 with a standard

deviation of 10; the scores were approximately normally distributed. The mean

score for the first 20 tests was 78. Did the students turning in their tests first score

significantly

different from the mean?

A national chain of women’s clothing stores with locations in the large shopping malls thinks that it can do a better job of planning more renovations and expansions if it understands what variables impact sales. It plans a small pilot study on stores in 25 different mall locations. The data it collects consist of monthly sales, store size (sq. ft), number of linear feet of window display, number of competitors located in mall, size of the mall (sq. ft),and distance to nearest competitor (ft).

1. Test the individual regression coefficients. At the 0.05 level of significance, what are your conclusions?

2. f you were going to drop just one variable from the model, which one would you choose? Why?

The store planners for the women’s clothing chain want to find the best model that they can for understanding what store characteristics impact monthly sales.

3. Use stepwise regression to find the best model for the data.

4. Analyze the model you have identified to determine whether it has any problem

5. Write a memo reporting your findings to your boss. Identify the strengths and weaknesses of the model you have chosen.

what does researcher looks for when manipulating a variable?

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 14, 16, 13, 7, 8.

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.)
s =

(b) Multiply each data value by 7 to obtain the new data set 98, 112, 91, 49, 56. Compute s. (Round your answer to one decimal place.)
s =

(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?

Multiplying each data value by the same constant c results in the standard deviation being |c| times as large.Multiplying each data value by the same constant c results in the standard deviation increasing by c units.    Multiplying each data value by the same constant c results in the standard deviation remaining the same.Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller.

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.9 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?

YesNo    

Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
s =  km

{4 marks} Here, we will quickly investigate the importance of understanding conditional prob- abilities when talking with medical patients. This problem is based on a true investigation by Hoffrage and Gigerenzer in 1996. The investigators asked practicing physicians to consider the following scenario:

“The probability that a randomly chosen woman age 40-50 has breast cancer is 1%. If a woman has breast cancer, the probability that she will have a positive mammogram is 80%. However, if a woman does not have breast cancer, the probability she will have a positive mammogram is 10%. Imagine that you are consulted by a woman, age 40-50, who has a positive mammogram but no other symptoms. What is the probability that she actually has breast cancer?”

Twenty-four physicians were asked to respond. The average probability estimate was 70%. Using your knowledge of Bayes’ Rule, determine if the physicians were close in their estimate. Comment on where the error in their judgement may have occurred, and why this may cause problems in their practice.

the probability of getting a single pair in a poker hand of 5 cards is approximately .42. Find the approximate probability that out of 1000 poker hands there will be at least 450 with a single pair.

1. The built-in data “trees” provide the measurements of diameter (Girth), height and volume of trees. These are in inches for Girth, feet for Height and cubic feet for Volume. We will focus on Girth and Height. Write a function convert() that converts the values into the metric system (meters). Your function should take as arguments the value to convert and the unit it was expressed in (inches or feet) (use the following: x inches = x*0.0254 meters, x feet = x*0.3048 meters). If the first argument is not numeric or if the second argument is not “inch” or “feet”, use stop() function with an error message. Here is how it should work:

> convert(8.3,"inches")

[1] 0.21082

> convert(8.3,"feet")

[1] 2.52984

> convert(8.3,"foot")

Error in convert(8.3, "foot") : the unit was not "inches" or "feet"

Use your function to convert the values of Girth and Height to meters. Using cor.test() function, calculate the correlation (and the corresponding p-value) between Girth and Height in meters.

What is "sampling bias"? Explain using proper terminology and craft your example to explain how it can affect the outcome of a statistical study. This should be several paragraphs long.

define p values. explain the two methods of interpreting p values

6.5.4

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Blood pressure is normally distributed.

1. State the random variable.
2. Suppose a sample of size 15 is taken. State the shape of the distribution of the sample mean.
3. Suppose a sample of size 15 is taken. State the mean of the sample mean.
4. Suppose a sample of size 15 is taken. State the standard deviation of the sample mean.
5. Suppose a sample of size 15 is taken. Find the probability that the sample mean blood pressure is more than 135 mmHg.
6. Would it be unusual to find a sample mean of 15 people in China of more than 135 mmHg? Why or why not?
7. If you did find a sample mean for 15 people in China to be more than 135 mmHg, what might you conclude?

6.5.6

The mean cholesterol levels of women age 45-59 in Ghana, Nigeria, and Seychelles is 5.1 mmol/l and the standard deviation is 1.0 mmol/l (Lawes, Hoorn, Law & Rodgers, 2004). Assume that cholesterol levels are normally distributed.

1. State the random variable.
2. Find the probability that a woman age 45-59 in Ghana has a cholesterol level above 6.2 mmol/l (considered a high level).
3. Suppose doctors decide to test the woman’s cholesterol level again and average the two values. Find the probability that this woman’s mean cholesterol level for the two tests is above 6.2 mmol/l.
4. Suppose doctors being very conservative decide to test the woman’s cholesterol level a third time and average the three values. Find the probability that this woman’s mean cholesterol level for the three tests is above 6.2 mmol/l.
5. If the sample mean cholesterol level for this woman after three tests is above 6.2 mmol/l, what could you conclude?

A simple random sample of size n equals n=400 individuals who are currently employed is asked if they work at home at least once per week. Of the 400 employed individuals​ surveyed, 40 responded that they did work at home at least once per week. Construct a​ 99% confidence interval for the population proportion of employed individuals who work at home at least once per week.

A population has a mean of 300 and a standard deviation of 90. Suppose a sample of size 125 is selected and is used to estimate . Use z-table.

What is the probability that the sample mean will be within +/- 3 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.) 0.8884 What is the probability that the sample mean will be within +/- 11 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)