Question

1. A city official claims that the proportion of all commuters
who are in favor of an expanded public transportation system is
50%. A newspaper conducts a survey to determine whether this
proportion is different from 50%. Out of 225 randomly chosen
commuters, the survey finds that 90 of them reply yes when asked if
they support an expanded public transportation system. Test the
official’s claim at α = 0.05.

2. A survey of 225 randomly chosen commuters are asked if they
support an expanded public transportation system. 90 said yes.
Construct a 95% confidence interval for the proportion of all
commuters who support expanded public transportation.

3. An industrial company claims that the mean pH level of the
water in a nearby river is 6.8. You randomly select 19 water
samples and measure the pH of each. The sample mean and the sample
standard deviation are 6.7 and 0.24, respectively. Is there enough
evidence at α = 0.05 to reject the claim that the pH level is 6.8?
Assume a normally distributed population.

4. You want to estimate the mean pH level of the water in a
nearby river. You randomly select 19 water samples and measure the
pH of each. The sample mean is 6.7 and the sample standard
deviation is 0.24. Construct a 95% confidence interval for the true
mean pH level.

5. Explain how using the same sample data and level of
significance to conduct a hypothesis test and to construct a
confidence interval can lead to the same conclusion. Use your work
in #1 − 4 to provide specific examples of the connections between
hypothesis tests and confidence intervals.

6. A sample of employees in a certain company gives the
following data about salaries. Answer the questions below based on
this data set.

$37,000 $95,000 $40,000 $39,750 $37,000 $38,600

(a) Calculate the mean. (b) Find the median.

(c) Find the mode.

(d) Which measure of central tendency you think best
represents the data? Explain WHY.

7. Use the following data set to complete the questions below.
Calculate the five number summary and sketch a box and whisker
plot. Be sure to label your box plot correctly.

78 74 76 80 85 81 62 80 91 46 20 94 95 96 91 82

(a) Calculate the five number summary.

(b) Calculate the interquartile range and determine any
potential outliers.

(c) Sketch a boxplot. Be sure to label your boxplot
correctly.

(d) Write one inference you can make about this data based on
your work above.

8. The lengths of pregnancies are normally distributed with a
mean of 267 days and a standard

deviation of 15 days.

(a) Find the probability that an individual woman has a
pregnancy shorter than 259 days.

(b) If 36 women are randomly selected, find the probability
that they have a mean preg- nancy shorter than 259 days.

(c) There should be a difference in your method for the
previous two questions. Explain what you did differently for each
problem and explain WHY your answers are different.

(d) Find the probability that an individual woman has a
pregnancy longer than 295 days.

(e) Find the probability that an individual woman has a
pregnancy between 259 and 295 days.

(f) What is the cutoff number of days for a pregnancy for the
top 15% of women?

(g) What is the cutoff number of days for a pregnancy for the
bottom 25% of women?

9. In the initial test of the Salk vaccine for polio, 400,000
children were selected and divided into two groups of 200,000. One
group was vaccinated with the Salk vaccine while the second group
was vaccinated with a placebo. Of those vaccinated with the Salk
vaccine, 33 later developed polio. Of those receiving the placebo,
115 later developed polio. Test the claim that the Salk vaccine is
effective in lowering the polio rate. Use α = 0.01.

10. Records of randomly selected births were obtained and
categorized according to the day of the week that they occurred
(based on data from the National Center for Health Statistics).
Because babies are unfamiliar with our schedule of weekdays, a
reasonable claim is that births occur on the different days with
equal frequency. Use a 0.01 significance level to test that
claim.

Day Sun Mon Tues Wed Thurs Fri Sat Number of Births 77 110 124
122 120 123 97

11. A study is conducted to find out whether the wait times at
two local banks are different. The sample statistics are listed
below. Test whether the wait times are the same or different
assuming that σ1=σ2. Use α = 0.05.

Bank 1

n1 = 15

x1 = 5.3 minutes s1 = 1.1 minutes

Bank 2

n2 = 16

x2 = 5.6 minutes s2 = 1.0 minutes

12. The health of the bear population in Yellowstone National
Park is monitored by periodic measurements taken from anesthetized
bears. A sample of 54 bears has a mean weight of 182.9 lb. Assume
that σ is known to be 121.8 lb.

(a) Use a 0.05 significance level to test the claim that the
population mean of all such bear weights is greater than 150 lb.
Use the usual critical-value method to perform this test.

(b) Find the P -value for this test and explain how the P
-value would lead you to the same conclusion that your rejection
region method did. (Note that you don’t have to re-do the whole
test, but show your work for finding the P -value.)

13. You are given the following regression equation for a
scatter plot which The displays data

for x = Weight of Car (in pounds) and y = Miles per Gallon in
City: y = −0.006x + 42.825 r2 = 0.7496

(Note: The scatter plot graph is attached to the Canvas
assignment as a separate document.)

(a) Find the value of r based on the information given.

(b) Based on your value of r, what conclusion can you make
about the correlation of this data?

(c) What does the value of r2 tell you about the
regression?

(d) Use the regression equation to estimate miles per gallon
for a car that weighs 3000

pounds.

(e) Use the regression equation to estimate the weight of a
car that gets 30 miles per gallon.

Answer #1

1. Given : n=225 , X=90

The estimate of the sample proportion is ,

The null and alternative hypothesis is ,

The test is two-tailed test.

The test statistic is ,

The critical values are , ; From Z-table

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , reject Ho.

Conclusion : There is sufficient evidence to support the claim that the proportion is different from 0.50

#1 Use the confidence level and sample data to find a confidence
interval for estimating the population μ. Find the margin of error
E and round your answer to the nearest tenth. Test scores: n = 93,
LaTeX: \bar{x}x ¯ = 88.5, σ = 6; 99% confidence
#2 A sociologist develops a test to measure attitudes towards
public transportation, and n = 82 randomly selected subjects are
given the test. Their mean score is LaTeX: \bar{x}x ¯ = 75.9 and...

The manufacturer of a new antidepressant claims that,
among all people with depression who use the drug, the proportion p
of people who find relief from depression is at least 80%. A random
sample of 205 patients who use this new drug is selected, and 160
of them find relief from depression. Based on these data, can we
reject the manufacturer's claim at the 0.05 level of significance?
Perform a one-tailed test. Then fill in the table below. Carry your...

A pharma company claims that there are at least 90 g of cream in
every jar. You decide to test the claim at a significance level
(alpha) of .05. You randomly sample 25 jars of cream made by the
company and find the sample mean to be 92.5 g with a sample
standard deviation of 5.5 g.
(a) What are the null and alternate hypotheses?
(b) Draw the picture of the distribution of the test statistic
(under H0). Include critical...

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,...

Let x be a random variable that represents the pH of arterial
plasma (i.e., acidity of the blood). For healthy adults, the mean
of the x distribution is μ = 7.4.† A new drug for arthritis has
been developed. However, it is thought that this drug may change
blood pH. A random sample of 31 patients with arthritis took the
drug for 3 months. Blood tests showed that x = 8.5 with sample
standard deviation s = 2.5. Use a...

Let x be a random variable that represents the pH of arterial
plasma (i.e., acidity of the blood). For healthy adults, the mean
of the x distribution is μ = 7.4.† A new drug for arthritis has
been developed. However, it is thought that this drug may change
blood pH. A random sample of 36 patients with arthritis took the
drug for 3 months. Blood tests showed that x = 8.6 with sample
standard deviation s = 3.2. Use a...

Part 1 Hypothesis Test and Confidence Interval from 1 sample
Test ONE claim about a population parameter by collecting your
own data or using our class survey data. Include your
written claim, hypothesis in both
symbolic and written form, relevant statistics
(such as sample means, proportions etc.), test
statistic, p-value (or critical value),
conclusion, and interpretation of
your conclusion in the context of your claim. Use a 0.05
significance level.
You will also construct a 95% confidence interval
estimate of...

Your task is to pick a hypothesis to test about a population
proportion (section 8.2) or a population mean (section 8.3). Once
you have determined your hypothesis you must go and collect the
data. Make sure your sample meets the requirements of a test
presented in sections 8.2 and 8.3 (such as appropriate sample
size). Use a 0.05 significance level.
Please clearly state the null and alternative hypotheses in
symbolic form and in words. State any relevant statistics from your...

i. A researcher estimated the proportion of voters who favor the
Democratic candidate in an election. Based on 500 people she
calculates the 95% confidence interval for the population
proportion p: 0.123 <p<0.181.
Which of the following is a valid interpretation of this
confidence interval ?______
a. There is a 95% chance that the true value of p lies between
0.123 and 0.181
b. If many different samples of 500 were selected
and a confidence interval was constructed based on...

A local newspaper claims in an article that the average income
for all handymen in the city is more than $5200 per month. A sample
of 20 randomly selected handymen had the mean income of $5300 with
the standard deviation of $150 per month. Test the claim made by
the local newspaper at α = 0.05 .
For each question you need to find the following
a) < 1 point > Write the given .
Step 1
b) < 2...

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