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:

1) A student at a four-year college claims that mean enrollment
at four-year colleges is higher than at two-year colleges in the
United States. Two surveys are conducted. Of the 35 four-year
colleges surveyed, the mean enrollment was 5,466 with a standard
deviation of 8,191. Of the 35 two-year colleges surveyed, the mean
enrollment was 5,068 with a standard deviation of 4,777. Test the
student's claim at the 0.10 significance level.
a) The null and alternative hypothesis would be:
H0:pF=pTH0:pF=pT...

Question 3
A college professor claims the proportion of students that
complete a homework assignment is 70%. To
test this claim, a random sample of students are monitored and
checked if they completed the home the algebra class.
Assume that the test statistic for this hypothesis test is
−1.73.
Since this is a two tailed hypothesis test, assume that the
critical values for this hypothesis test are −1.96 and 1.96.
Come to a decision for the hypothesis test and interpret...

A professor at a small college suspects that poor readers may
test lower in IQ than those whose reading is “satisfactory.”
(Possibly AT grade level?) She draws a random sample of 28 students
who are labeled as “poor readers.” She examines the data in the
historical archives and finds a population mean IQ of 105. The
sample of 28 has a mean of 103.8 with a sample standard deviation
of 1.42. Again using a level of significance of 0.05, test...

1. Numerous studies have shown that IQ scores have been
increasing, generation by generation, for years. The increase is
called the Flynn Effect, and the data indicate that the increase
appears to be about 7 points per decade. To demonstrate this
phenomenon, a researcher obtains an IQ test that was written in
1980. At the time the test was prepared, it was standardized to
produce a population mean of µ = 100 and σ = 15. The researcher
administers the...

A college professor claims that the entering class this year
appears to be smarter than entering classes from previous years. He
tests a random sample of
10
of this year's entering students and finds that their mean IQ
score is
121
, with standard deviation of
14
. The college records indicate that the mean IQ score for
entering students from previous years is
111
. If we assume that the IQ scores of this year's entering class
are normally...

The registrar claims that the mean IQ of students at Stetson
University (μ_0) is 120 with a standard deviation (σ) of 10. You
obtain a random sample of 25 students and find that their mean (X ̅
) is 115.State the null and alternative hypotheses. Conduct a z
test to evaluate the registrar’s claim. Let α=.05. Please show your
work and be sure to provide the z statistic, critical z value, and
p value. What decision do you make about...

Question1: It is known the population IQ score follows a normal
distribution with mean as 100, SD as 10. A researcher is interested
in studying if the average IQ of students from statistics courses
on average has a higher IQ score than the population IQ score. To
test this hypothesis, the researcher randomly collected a sample of
25 students from statistic class, the mean IQ score for this sample
is 110. Compete for the hypothesis test at significant level.
Step...

The accompanying data table lists the weights of male college
students in kilograms. Test the claim that male college students
have a mean weight that is less than the 8383 kg mean weight of
males in the general population. Use a 0.010.01 significance level.
Identify the null hypothesis, alternative hypothesis, test
statistic, P-value, and conclusion for the test. Assume this is a
simple random sample. Calculate the test statistic (round to three
decimals) That is the P value?

IQ scores among the general population have a mean of
100
and a standard deviation of
15
. A researcher claims that the standard deviation,
σ
, of IQ scores for males is less than
15
. A random sample of
16
IQ scores for males had a mean of
98
and a standard deviation of
10
. Assuming that IQ scores for males are approximately normally
distributed, is there significant evidence (at the
0.1
level of significance) to conclude...

A college professor claims that the entering class this year
appears to be smarter than entering classes from previous years. He
tests a random sample of 15 of this year's entering students and
finds that their mean IQ score is 113, with standard deviation of
15. The college records indicate that the mean IQ score for
entering students from previous years is 112. If we assume that the
IQ scores of this year's entering class are normally distributed,
is there...

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