Question

In: Statistics and Probability

We are testing the hypothesis of no difference between means of two normally distributed populations (eg...

We are testing the hypothesis of no difference between means of two normally distributed populations (eg number of cracks in bricks). Alternative hypothesis is inequality. Significance is .05. Samples from these populations are X {3,5,6,9] and Y [6,11,15,21]

Sample correlation coefficient p=.993 , V(x) = 6.25 and V(Y) = 40.25

What test is appropriate (explain)?

Calculate appropriate test statistic (two tailed) and the P-Value using table?

State Conclusion

Solutions

Expert Solution

What test is appropriate (explain)?

The most appropriate test is the t test for two independent samples for the difference of means. This is because the sample size is small and the parents distributions are normal.

Calculate appropriate test statistic (two tailed) and the P-Value using table?

the t-statistic is computed as follows:

The p-value is p = 0.0701

Since it is observed that ∣t∣=2.2≤tc​=2.447, it is then concluded that the null hypothesis is not rejected.

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

Please let me know in comments if anything is unclear. Will reply ASAP. Please upvote if satisfied!


Related Solutions

In testing the difference between the means of two normally distributed populations, if μ1 = μ2...
In testing the difference between the means of two normally distributed populations, if μ1 = μ2 = 50, n1 = 9, and n2 = 13, the degrees of freedom for the t statistic equals ___________. 19,20,21,22 When comparing two independent population means by using samples selected from two independent, normally distributed populations with equal variances, the correct test statistic to use is ______. z,F,t, t^2 When testing a hypothesis about the mean of a population of paired differences in which...
Hypothesis Testing and Confidence Intervals for Proportions and Hypothesis Test for Difference between Two Means A...
Hypothesis Testing and Confidence Intervals for Proportions and Hypothesis Test for Difference between Two Means A pharmaceutical company is testing a new cold medicine to determine if the drug has side affects. To test the drug, 8 patients are given the drug and 9 patients are given a placebo (sugar pill). The change in blood pressure after taking the pill was as follows: Given drug: 3 4 5 1 -2 3 5 6 Given placebo: 1 -1 2 7 2...
Suppose we are interested in testing null hypothesis that difference of two population means is the...
Suppose we are interested in testing null hypothesis that difference of two population means is the same. Consider two samples collected from a normal population. x 4.2 4.5 4.9 5.6 5.7 5.9 6.1 6.3 6.8 7.1 7.3 7.8 8.4 8.6 9.1 9.7 10.2 y 5.6 5.9 6.5 7.8 8.5 9.3 We need to testH0:x=yvsHa:x̸=yWe can use R-command t.test to compute the p-value and the confidence interval.> x = c ( 4.2 ,4.5,4.9,5.6,5.7 ,5.9, 6.1, 6.3 , 6.8 , 7.1 ,...
This assignment uses hypothesis testing to determine if there is a significant difference between the means...
This assignment uses hypothesis testing to determine if there is a significant difference between the means of three or more groups. Find solutions to the following problems. Be sure to include a statement about significance and complete a Tukey's HSD when necessary. Subjects were interviewed about their smoking habits in cigarettes per day and were tested for their aerobic capacity. Taking cigarettes per day as the explanatory (independent) variable and aerobic capacity as the response (dependent) variable, find the correlation...
Consider the following statements. (i). If we are testing for the difference between two population means,...
Consider the following statements. (i). If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population. (ii). If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances. (iii). The critical value of t for a two-tail test of the difference of two means, a level...
In constructing 95% confidence interval estimate for the difference between the means of two populations, where...
In constructing 95% confidence interval estimate for the difference between the means of two populations, where the unknown population variances are assumed not to be equal, summary statistics computed from two independent samples are: ?1=45,?̅1=756,?1=18,?2=40,?̅2=762,?2=15 (using 2-sample T menu) a. Calculate the 95% confidence interval for the true difference of two means. b. Base on the interval in the previous question, can one conclude there is a difference in means of two populations? Justify your answer.
Two independent random samples were selected from two normally distributed populations with means and variances (μ1,σ21)...
Two independent random samples were selected from two normally distributed populations with means and variances (μ1,σ21) and (μ2,σ22). The sample sizes, means and variances are shown in the following table. Sample 1 n1 = 13 x̄1 = 18.2 s21 = 75.3 Sample 2 n2 = 14 x̄2 = 17.1 s2= 61.3 (a). Test H0 : σ12 = σ2against Ha : σ12 ̸= σ2. Use α = 0.05. Clearly show the 4 steps. (b). TestH0 :μ1 −μ2 =0againstHa :μ1 −μ2 >0....
Discuss why we would expand the idea of hypothesis testing to two populations. Can you provide...
Discuss why we would expand the idea of hypothesis testing to two populations. Can you provide an example of this type of hypothesis testing?
Hypothesis testing is based on the idea that if there is enough of a difference between...
Hypothesis testing is based on the idea that if there is enough of a difference between your experimental sample and the comparison distribution, you can see the research supports your hypothesis. Describe an experiment in which you would expect there to be a very small difference between the experimental sample and the comparison distribution. How small of a difference could there be for you to still be okay with rejecting the null hypothesis?
Perform a hypothesis test (comparing means) on the two populations below. Assume equal means and normal...
Perform a hypothesis test (comparing means) on the two populations below. Assume equal means and normal distribution. Population A Population B 42 65 41 22 50 51 25 17 78 24 35 57 19 67 22 26 45 88 45 85
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT