Question

- Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume the population standard deviations are equal.

Suppose you are interested if a name brand candle is made from the same wax as the generic store brand candle. You decide that they smell the same, so the only question left is if they last as long as a generic brand candle (of the same size, type). These two brands of candles are tested and the average time they burned (in hours) are recorded. The summary statistics are given below:

Name Brand |
Generic Store Brand |

n=35 |
n=40 |

19.4 hours |
15.1hours |

s=1.4 hours |
s=0.8 hours |

Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean (indicating that there is no difference in the population means). Perform a complete hypothesis test, including a diagram of the critical values.

Answer #1

Test the indicated claim about the means of two populations.
Assume that the two samples are independent simple random samples
selected from normally distributed populations. Do not assume that
the population standard deviations are equal. Use the traditional
method. 1) A researcher was interested in comparing the response
times of two different cab companies. Companies A and B were each
called at 50 randomly selected times. The calls to company A were
made independently of the calls to company B....

it's important - give your best please :)
Test the claim that the samples come from populations with the
same mean. Assume that the populations are normally distributed
with the same variance.
Given the sample data below, test the claim that the population
have the same mean. Use a significance level of 0.05.
Brand A
Brand B
Brand C
Brand D
n=16
n=16
n=16
n=16
=2.09
=3.48
=1.86
=2.84
s=0.37
s=0.61
s=0.45
s=0.53

Construct the indicated confidence interval for the difference
between the two population means. Assume that the two samples are
independent simple random samples selected from normally
distributed populations. Do not assume that the population standard
deviations are equal.
Two types of flares are tested and their burning times are
recorded. The summary statistics are given below.
Brand X
Brand Y
n = 35
n = 35
x-bar = 19.4 min
x-bar = 15.1 min
s = 1.4 min
s =...

Consider the test of the claims that the two samples described
below come from two populations whose means are equal vs. the
alternative that the population means are different. Assume that
the samples are independent simple random samples and that both
populations are approximately normal with equal variances. Use a
significance level of α=0.05 Sample 1: n1=18, x⎯⎯1=28, s1=7 Sample
2: n2=4, x⎯⎯2=30, s2=10
(a) Degrees of freedom =
(b) The test statistic is t =

. Assume the samples are from populations that are normally
distributed. Construct the indicated confidence intervals for both
(a) the population variance σ 2 and (b) the population standard
deviation σ.
c = 0.99, s = 5.7, n = 42

Use the traditional method of hypothesis testing to test the
given claim about the means of two populations. Assume that two
dependent samples have been randomly selected from normally
distributed populations.
The table below shows the weights of seven subjects before and
after following a particular diet for two months.
Subject A B C D E F G
Before: 182 178 199 194 151 188 170
After: 175 169 197 199 137 190 158
Using a 0.01 level of significance,...

Independent random samples are selected from two populations.
The summary statistics are given below. Assume unequal variances
for the questions below. m = 5 x ̅ = 12.7 s1 = 3.2
n = 7 y ̅ = 9.9 s2 = 2.1
a) Construct a 95% confidence interval for the difference of the
means.
b) Using alpha = 0.05, test if the means of the two populations
are different based on the result from part (a). Explain your
answer.

Two random samples are selected from two independent
populations. A summary of the samples sizes, sample means, and
sample standard deviations is given below:
n1=45,n2=40,x¯1=50.7,x¯2=71.9,s1=5.4s2=10.6 n 1 =45, x ¯ 1 =50.7, s
1 =5.4 n 2 =40, x ¯ 2 =71.9, s 2 =10.6
Find a 92.5% confidence interval for the difference μ1−μ2 μ 1 −
μ 2 of the means, assuming equal population variances.

Perform the indicated hypothesis test. Assume that the
two samples are independent simple random samples selected from
normally distributed populations.
1) A researcher was interested in comparing the amount of time
spent watching television by women and by men. Independent simple
random samples of 14 women and 17 men were selected, and each
person was asked how many hours he or she had watched television
during the previous week. The summary statistic are as follows.
Women: xbar1= 12.2hr s1= 4.4...

Test the given claim using the α=0.01 significance
level and assuming that the populations are normally
distributed.
Claim: The treatment population and the placebo population have the
same mean.
Treatment group: n=6, x¯=119,
s=5.8.
Placebo group: n=13, x¯=112, s=5.6.
(a) The test statistic
is .
(b) What is the
conservative estimate for the degrees of freedom? df =
(c) The negative
critical value is .
(d) The positive
critical value is .
(e) Is there
sufficient evidence to warrant the...

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