Question

Two different hardening processes, (1) saltwater quenching and (2) oil quenching, are used on samples of a particular type of metal alloy. The results are shown in the following table. Assume that hardness is normally distributed. (1) Assuming that the variances ?ଵ ଶ and ?ଶ ଶ are equal, construct a 95% confidence interval on the difference in mean hardness. (2) Construct a 90% confidence interval on the ratio ?ଵ ଶ ?ଶ ൘ ଶ. Does the assumption made earlier of equal variances seem reasonable?

Answer #1

Assuming Data is

a)

b)

CI = (0.3054,3.0864)

yes, because 1 is present in confidence interval

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Two different hardening processes (1) saltwater quenching and
(2) oil quenching , are used on sample of particular metal alloy.
the hardness test results of samples are shown on the table.
Salt water quench 145,150,153,148,141,152,146,154,139,148
Oil quench 152, 150, 147,155,140,146,158,152,151,143
Calculate mean values and standard deviation of two
processes
Construct a 95% confidence between two mean values
Chech whether std dev(a) a1^2=a2^2
Test the hypothesis that the mean hardeness for saltwater
quenching equals oil quenching process. Mar the regions in...

6. Given two independent random samples with the following
results: ?ଵ = 7 ?̅ଵ = 103 ?ଵ = 34 Use this data to find the 90%
confidence interval for the true difference between the population
means. Assume that the population variances are not equal and that
the two populations are normally distributed. ?ଶ = 12 ?̅ଶ = 82 ?ଶ =
15 Step 1. Find the point estimate that should be used in
constructing the confidence interval. Answer: ____________________
Step 2....

Consider the following data from two independent samples with
equal population variances. Construct a 90% confidence interval to
estimate the difference in population means. Assume the population
variances are equal and that the populations are normally
distributed.
x1 = 37.1
x2 = 32.2
s1 = 8.9
s2 = 9.1
n1 = 15
n2 = 16

Given two independent random samples with the following results:
n1=11 x‾1=131 s1=30 n2=13 x‾2=162 s2=33 Use this data to find the
95% confidence interval for the true difference between the
population means. Assume that the population variances are not
equal and that the two populations are normally distributed.
Step 1 of 3: Find the point estimate that should be used in
constructing the confidence interval.
Step 2 of 3: Find the margin of error to be used in constructing
the...

Given two independent random samples with the following
results:
n1=7
x‾1=129
s1=14
n2=14
x‾2=159
s2=24
Use this data to find the 95% confidence interval for the true
difference between the population means. Assume that the population
variances are not equal and that the two populations are normally
distributed.
Step 1 of 3:
Find the point estimate that should be used in constructing the
confidence interval.
Step 2 of 3:
Find the margin of error to be used in constructing the...

Given two independent random samples with the following
results:
n1=11
x‾1=128
s1=23
n2=13
x‾2=110
s2=32
Use this data to find the 95%95% confidence interval for the
true difference between the population means. Assume that the
population variances are equal and that the two populations are
normally distributed.
Copy Data
Step 1 of 3:
Find the critical value that should be used in constructing the
confidence interval. Round your answer to three decimal places.
Step 2 of 3:
Find the standard...

Given two independent random samples with the following results:
n1=11x‾1=80s1=28 n2=9x‾2=99s2=18 Use this data to find the 90%
confidence interval for the true difference between the population
means. Assume that the population variances are equal and that the
two populations are normally distributed. Step 1 of 3 : Find the
critical value that should be used in constructing the confidence
interval. Round your answer to three decimal places

Exercise 2. The following information is based on independent
random samples taken from two normally distributed populations
having equal variances:
Sample 1
Sample 2
n1= 15
n2= 13
x1= 50
x2= 53
s1= 5
s2= 6
Based on the sample information, determine the 90% confidence
interval estimate for the difference between the two population
means.

Given two independent
random samples with the following results:
n1=9
n2=13
x‾1=153 x‾2=113
s1=30
s2=26
Use this data to find
the 95% confidence interval for the true difference between the
population means. Assume that the population variances are not
equal and that the two populations are normally distributed.
Copy Data
Step 2 of 3 :
Find the margin of
error to be used in constructing the confidence interval. Round
your answer to six decimal places.

Given two independent random samples with the following
results:
n1
=
11
n2
=
13
xbar1
=
162
xbar^2
=
130
s1
=
31
s2
=
30
Use this data to find the 95% confidence interval for the true
difference between the population means. Assume that the population
variances are equal and that the two populations are normally
distributed.
Copy Data
Step 1 of 3: Find the critical value that should be used in
constructing the confidence interval. Round...

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