# Exam 2

**Topics:**Arithmetic mean, Mean, Normal distribution

**Pages:**11 (2016 words)

**Published:**January 16, 2012

PUBH 600

Guidelines: You may use all of the resources (e.g., textbook, other books, websites) available to you, EXCEPT FOR OTHER PEOPLE. Your work must be done individually. Any exams that appear similar in format and/or answers will be considered to have been done in a group setting. All such exams will receive a score of 0. Late exams will not be accepted for any reason. Any late exams will receive a score of 0. These policies will be strictly enforced. Remember that your exam must be typed in a Word document. Do not save your work as Word 2007. The exam can either be submitted as an attachment through WebCT or a hardcopy can be submitted to me in my office before 5:00 pm on November 20. Completed exams will be accepted at any time until the deadline.

Each question is worth 10 points.

1.Suppose the distribution of serum cholesterol values in undergraduate men is approximately normal with mean ( = 190 mg/dl and standard deviation ( = 40 mg/dl. a. What is the probability of selecting someone at random from this population who has a cholesterol value that is less than 180?

[pic]

b. You take a simple random sample of n = 49 individuals from this population and calculate the mean cholesterol of the sample. Describe the sampling distribution of xbar.

The standard deviation of the sampling distribution of x-bar is called the SE and is = [pic]

c. Regarding the mean derived from a sample of n = 49, what is the probability of getting a sample mean that is less than 180? [Determine Pr(xbar < 180)].

[pic]

2.Based on prior studies, a dental researcher is willing to assume that the standard deviation of the weekly sugar consumption in children in a particular community is 100 grams. How large a sample is needed to estimate mean sugar consumption in the community with a margin of error 10 grams at 95%?

[pic]

3. Based on prior studies, a dental researcher is willing to assume that the standard deviation of the weekly sugar consumption in children in a particular community is 100 grams. How many kids should be studied if the researcher is willing to accept a margin of error of 25 grams at 95%?

[pic]

4.The manufacturer of a laboratory scale claims their scale is accurate to within 0.0015 gram. You read the documentation for the scale and learn that this means that the standard deviation of an individual measurement (() is equal to 0.0015 grams. Assume measurements vary according to a normal distribution with µ equal to the actual weight of the object. You weigh the same specimen twice and get readings of 24.31 grams and 24.34 grams. Based on this information, calculate a 95% confidence interval for the true weight of the object.

[pic]

5.The 95% confidence interval for the mean weight of infants born to mothers who smoke is 5.7 to 6.5 pounds. The mean weight for all newborns in this region is 7.2 pounds. Is the birth weight of the infants in this sample significantly different from that of the general population at ( = 0.05? Explain your response.

Sample mean is the center of the confidence interval

xbar = [pic]

A 95% confidence interval corresponds to

( = 0.05

Therefore, if the 95% CI for [pic]=6.1 = 5.7 to 6.5 pounds, the sample mean is significantly different because it excludes 7.2 pounds.

6.The placebo effect occurs when a patient experiences a perceived benefit after receiving an inert substance. To help understand the mechanism behind this phenomenon in Parkinson’s disease patients, investigators measured striatal RAC binding at a key point in the brains in six subjects. RAC binding was reduced by an average of 0.326 units (dbar) on a placebo in the six subjects (sd = 0.181). Test this difference for statistical significance.

[pic]

7.The calcium content values in a sample of n = 5 sound teeth (%...

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