In a two sample problem where the null hypothesis states that µ1 = µ2, we obtained...
In a two sample problem where the null hypothesis states that µ1 = µ2, we obtained the sample statistics ¯x1 = 32.86, x¯2 = 35.62, if the test statistic is significant (which means in the rejection region), then a proper conclusion would be:
A. The two means are equal
B. The two means could be equal
C. The first mean is less than the second mean
Homework Answers
We have given, test statistic is significant.
i.e. Reject the null hypothesis.
| C. The first mean is less than the second mean |
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In a two sample problem where the null hypothesis states that µ1
= µ2, we obtained...
A researcher poses a null hypothesis of H0: µ1 ≤ µ2, and a research hypothesis of...
A researcher poses a null hypothesis of H0: µ1 ≤ µ2, and a research hypothesis of H1: µ1 > µ2. The researcher selects an α = 0.05 critical threshold. The test has 11 degrees of freedom. The researcher obtains a t-statistic of 1.67. Determine which course of action is most appropriate. Reject the null hypothesis. Do not reject the null hypothesis. Cannot determine with the information given.
A researcher poses a null hypothesis of H0: µ1 ≤ µ2, and a research hypothesis of...
A researcher poses a null hypothesis of H0: µ1 ≤ µ2, and a research hypothesis of H1: µ1 > µ2. The researcher selects an α = 0.05 critical threshold. The test has 11 degrees of freedom. The researcher obtains a t-statistic of 1.67. Determine which course of action is most appropriate.
The null and alternate hypotheses are: H0:µ1≤µ2. H0:µ1>µ2. A random sample of 29 items from the first population show...
The null and alternate hypotheses are: H0:µ1≤µ2. H0:µ1>µ2. A random sample of 29 items from the first population showed a mean of 112 and a standard deviation of 9. A sample of 15 items for the second population showed a mean of 97 and a standard deviation of 12. Use the .01 significance level. a. Find the degrees of freedom for unequal variance test b. State the decision rule for .1 significance level c. Compute the value of the test...
Problem 3. Consider two independent samples, X1, . . . , Xm from a N(µ1, σ12 ) distribution and Y1, . . . , Yn from a N(µ2, σ22 ) distribution. Here µ1, µ2, σ12 and σ2 are unknown. Consider testing th...
Problem 3. Consider two independent samples, X1, . . . , Xm from a N(µ1, σ12 ) distribution and Y1, . . . , Yn from a N(µ2, σ22 ) distribution. Here µ1, µ2, σ12 and σ2 are unknown. Consider testing the null hypothesis that the two population variance are equal, H0 : σ12 = σ22 , against the alternative that these variances are different, H1 : σ12 ≠ σ12 . (a) Derive the LR test statistic Λ
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Null hypothesis: products equally Alternative hypothesis: #2 sells cheaper than #1 H0: µ1 = µ2, Ha: µ1 > µ2 N=20 Please assist in finding the following: random predicted outcome. second outcome of 16/20 statistic difference sample difference standard error df standardized statistics p-value standard deviation standard error confidence interval within 95% product name stat 1 stat 2 Price Comparison a $ 14.39 $ 10.39 $ 4.00 b $ 14.39 $ 10.94 $ 3.45 c $ 9.99 $ 9.99 $ - ...
Suppose you want to test the claim that µ1 < µ2. Two samples are randomly selected...
Suppose you want to test the claim that µ1 < µ2. Two samples
are randomly selected from each population. The sample statistics
are given below. At a level of significance of α = 0.05, when
should you reject H0?
n1 = 35
n2 = 42
x̅1 = 29.05 x̅2 =
31.6
s1 =
2.9
s2 = 2.8
Suppose you want to test the claim that u1<p2. Two samples are randomly selected from each population. The sample statistics are given...
please answer both with an explanation (14) For testing Ho : µ1 = µ2 versus H1...
please answer both with an explanation
(14) For testing Ho : µ1 = µ2 versus H1 : µ1 # µ2, a completely randomized design used two indpendent samples of sizes n = m = 10 and obtained t-statistics = -2.87. If the assumption of equal but unknown population variances is justified, what is the p-value? The following "answers" have been proposed. (a) Approximately 0.005 (b) Approximately 0.01 (c) Approximately 0.025 (d) Approximately 0.05 (e) None of the above. The correct...
Analysis of a random sample consisting of m = 20 specimens of cold-rolled steel to determine yield strengths resulted in a sample average strength of ¯x = 29.8 ksi. A second random sample of n = 25 two-sided galvanized steel specimens gave a sample averag
Analysis of a random sample consisting of m = 20 specimens of cold-rolled steel
to determine yield strengths resulted in a sample average strength of ¯x = 29.8 ksi.
A second random sample of n = 25 two-sided galvanized steel specimens gave a
sample average strength of ¯y = 34.7 ksi. Assuming that the two yield-strength
distributions are normal with σ1 = 4.0 and σ2 = 5.0.(a) Find the 99% confidence interval of the difference µ1 − µ2 between the...
Consider a situation where we want to compare means, M1 and 42 of two populations, Group...
Consider a situation where we want to compare means, M1 and 42 of two populations, Group 1 and Group 2, respectively. A random sample of 40 observations was selected from each of the two populations. The following table shows the two-sample t test results at a = 5% assuming equal population variances: t-Test: Two-Sample Assuming Equal Variances Group 2 28652 33.460 40 Mean Variance Observations Pooled Variance Hypothesized Mean Difference d t Stat PTcut) one-tail Critical one-tail PTC-t) two-tail Critical...
Test the claim about the difference between the two population means µ1 and µ2 at the...
Test the claim about the difference between the two
population means µ1 and µ2 at the level of significance α.
Important! Please remember to include all 5 parts of a hypothesis
test mentioned in the module summary. Assume the samples are random
and independent, and the populations are normally
distributed.
Exercise 5. Claim: /142; a = 0.05. Assume o o%. Sample statistics: = 97.6, s1 = 5.8, n1 = 33, T2 = 94.1,82 = 6.5, and n2 = 28 Exercise...
Suppose you want to test the claim that µ1 < µ2. Two samples
are randomly selected from each population. The sample statistics
are given below. At a level of significance of α = 0.05, when
should you reject H0?
n1 = 35
n2 = 42
x̅1 = 29.05 x̅2 =
31.6
s1 =
2.9
s2 = 2.8
Suppose you want to test the claim that u1<p2. Two samples are randomly selected from each population. The sample statistics are given...
please answer both with an explanation
(14) For testing Ho : µ1 = µ2 versus H1 : µ1 # µ2, a completely randomized design used two indpendent samples of sizes n = m = 10 and obtained t-statistics = -2.87. If the assumption of equal but unknown population variances is justified, what is the p-value? The following "answers" have been proposed. (a) Approximately 0.005 (b) Approximately 0.01 (c) Approximately 0.025 (d) Approximately 0.05 (e) None of the above. The correct...
Consider a situation where we want to compare means, M1 and 42 of two populations, Group 1 and Group 2, respectively. A random sample of 40 observations was selected from each of the two populations. The following table shows the two-sample t test results at a = 5% assuming equal population variances: t-Test: Two-Sample Assuming Equal Variances Group 2 28652 33.460 40 Mean Variance Observations Pooled Variance Hypothesized Mean Difference d t Stat PTcut) one-tail Critical one-tail PTC-t) two-tail Critical...
Test the claim about the difference between the two
population means µ1 and µ2 at the level of significance α.
Important! Please remember to include all 5 parts of a hypothesis
test mentioned in the module summary. Assume the samples are random
and independent, and the populations are normally
distributed.
Exercise 5. Claim: /142; a = 0.05. Assume o o%. Sample statistics: = 97.6, s1 = 5.8, n1 = 33, T2 = 94.1,82 = 6.5, and n2 = 28 Exercise...
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