Question

Assume that the speeds at which all men and all women drive cars on this highway are both approximately normally distributed with unknown and unequal population standard deviations. a. Construct a 98% confidence interval for the difference between the mean speeds of cars driven by all men and all women on this highway. b. Test at a 1% significance level whether the mean speed of cars driven by all men drivers on this highway is higher than that of cars driven by all women drivers. c. Suppose that the sample standard deviations were 1.9 and 3.4 miles per hour, respectively. Redo parts a and b. Discuss any changes in the results.

n1 = 27 n2= 18 x1 = 72 x2 = 68 s1 = 2.2 s2 = 2.5

Answer #1

a)

t valuee at 98% = 2.5669

CI = (x1 -x2) +/- t *sqrt(s1^2/n1+s2^2/n2)

= (72 - 68) +/- 2.5669 *sqrt(2.2^2/27 + 2.5^2/18)

= (2.1375,5.8625)

b)

H0 : mu1 = mu2

Ha: mu1 > mu2

test statistics:

t = (x1 -x2)/sqrt(s1^2/n1+s2^2/n2)

=(72 - 68) /sqrt(2.2^2/27 + 2.5^2/18)

= 5.5128

p value = 0.00001

Reject H0

c)

t valuee at 98% = 2.5669

CI = (x1 -x2) +/- t *sqrt(s1^2/n1+s2^2/n2)

= (72 - 68) +/- 2.5669 *sqrt(1.9^2/27 + 3.4^2/18)

= (1.7389,6.2611)

b)

H0 : mu1 = mu2

Ha: mu1 > mu2

test statistics:

t = (x1 -x2)/sqrt(s1^2/n1+s2^2/n2)

= (72 - 68) /sqrt(1.9^2/27 + 3.4^2/18)

= 4.5410

p value = 0.00001

Reject H0

Refer to speeds at which cars pass through a checkpoint on the
highway. Assume the speeds are normally distributed with a
population mean of 61 miles per hour and a population standard
deviation of 4 miles per hour. Calculate the probability that the
next car passing will be travelling more than 58 miles per
hour.

The heights of randomly selected men and women were recorded.
The summary statistics are below. Construct a 90% confidence
interval for the difference between the mean height (in cm) of
women and the mean height of men. Assume that the two samples are
independent and that they have been randomly selected from normally
distributed populations. Do not assume that the population standard
deviations are equal. Women n1=10 x1=162.4cm s1= 11.8cm Men n2=10
x2=10 s2=5.3cm

3. A study done on body temperatures of men and women. The
results are shown below: Assume that the two samples are
independent simple random samples selected from normally
distributed populations, and do not assume that the population
standard deviations are equal. Use a 0.05 significance level To
test the claim that men have a higher mean body temperature than
women. μ1 n1 = 11 X1 = 97.57 S1 = 0.78 degree F degree F μ2 n2 = 59
X2...

For all hypothesis tests: Assume all samples are simple
random samples selected from normally distributed populations. If
testing means of two independent samples, assume variances are
unequal. For each test give the null and alternative hypothesis,
p-value, and conclusion as it relates to the claim.
In a random sample of 360 women, 65% favored stricter gun
control laws. In a random sample of 220 men, 60% favored stricter
gun control laws. Test the claim that the proportion of women
favoring...

Would Not Approve of Driving
Drunk
Would Not Care or Would Approve of Driving
Drunk
n1=40
n2=25
X¯1=2.1
X¯2=8.2
s1=1.8
s2=1.9
John Worrall and colleagues (2014) found that the fear of losing
the good opinion of one’s family and peers kept people from driving
home drunk. Let’s say we have two independent random samples of
people: those who think that their peers would disapprove of them
from driving drunk, and those who think that their peers would
either not care...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 21 minutes ago

asked 24 minutes ago

asked 27 minutes ago

asked 37 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago