Question

BIOS 376 Homework 7

1. A professor claims that the mean IQ for college students is 92. He collects a random sample of 85 college students to test this claim and the mean IQ from the sample is 84.

(a) What are the null and alternative hypotheses to test the initial claim? (1 pt)

(b) Using R, compute the test statistic. Assume the population standard deviation of IQ scores for college students is 17.6 points. (1 pt)

(c) Using R, find the p-value to test the claim at the 0.01 level of significance. Show/explain how you found these values. (1 pt)

(d) Find a conclusion for the test (i.e., reject or fail to reject the null hypothesis). State your reasoning (i.e., why?). (1 pt)

(e) Interpret your conclusion from part (d) by putting your results in context of the initial claim. Use complete sentences and see the textbook for examples. (1 pt)

2. Suppose you are NOT given population standard deviation but are told that the sample standard deviation is 17.5. Using R, perform hypothesis testing for the last problem. Make sure you state all five steps. (3 pts)

3. Aiming to investigate the relationship between overall well-being and job stress, researchers administered the Health-Related Quality of Life (HR-QOL) to a sample of 35 working individuals who described their work environment as high stress. HR-QOL scores are scaled to be between 0 and 100. A score of 0 indicates low quality of life and 100 indicates high quality of life. They originally thought that the mean HR-QOL score for the population of those working in high stress environments should be less than a score of 40. The sample resulted in a mean of 39.1 points and a sample standard deviation of 5.10 points. Using a significance level of 0.05, test the researchers’ hypothesis (using R). Show all work and assumptions. Clearly follow the 5 step process. (5 pts)

4. Low birth weight (¡2500 grams) can cause serious health problems during growth. Birth weight data for 175 newborns were collected from a hospital. Based on the demographics the researchers hypothesized that low birth weight should be rare in this population and the mean birth weight should be within the normal range. Use the data file ”lbw.RData” from the ”Datasets” folder on D2L to test the researchers’ hypothesis in R and interpret the results. Carefully write what the null and alternative hypotheses are and choose the correct R command. Clearly highlight or state the p-value. The variable for birth weight is called ”BWT”. R is case sensitive. (4 pts)

5. Determine for each scenario if you would use a normal (z) distribution, t-distribution, or if nonparametric methods must be used. Provide a simple explanation. (1 pt each) • H0: µ=2.55 H1: µ 6= 2.55. Sample data: n=7, ¯x=2.41, s=0.66. The sample data appear to come from a normally distributed population with unknown µ and σ. 1-1 1-2 • H0: µ=0.0105 H1: µ ¿ 0.0105. Sample data: n=17, ¯x=0.0134, s=0.0022. The sample data appear to come from a population with a distribution that is bimodal, and σ is unknown. • H0: µ=75 H1: µ ¿ 75. Sample data: n=15, ¯x=66, s=12. The sample data appear to come from a normally distributed population with σ=14.

6. A survey showed that among 568 randomly selected subjects who completed four years of college, 498 are employed full time. Assume the full time employment rate for the population is 83%. Use a 0.01 significance level to test the claim (suing R) that the rate of employment (proportion unemployed) among those with four years of college is different than the rate for the general population. Clearly follow the 5 step process. (5 pts)

Answer 1

1(a)

Hypotheses are:

(b)

The test statistics is

z = -4.19

(c)

The p-value is : 0.0000

(d)

Since p-value is less than 0.01 so we reject the null hypothesis.

(e)

There is not sufficient evidence to support the professor claims that the mean IQ for college students is 92.

Following is the screen shot r script:

Following is the output: