Statistics - Two Sample Hypothesis Test- using t-statistic

Question :

In comparing purchases from 2 companies, a sample of 16 purchases from Cambells with the mean $ 11, 045 and Standard Deviation of $ 835 is taken. For a sample of 18 purchases from Rainer mean cost is $ 12,840 and Standard Deviation is $ 1545.
At the 5% significance level, can we conclude that the cost from Rainer is higher?

Let Mu1 denote the mean purchases from Rainer and, Mu2 denotes the mean purchases from Cambells.
We have to decide between the ...

Solution Summary

Solution to the posted problem is given step by step with explanation and working. Two Samples of sizes 16 and 18 are used with Sample Means, Sample Standard Deviations to Test the Difference between Population Means or in other words, to compare population means at 5% Significance level. Every minute detail is explained in a simple way as how to find the degrees of freedom, how to find the test-statistic, how to formulate the decision hypothesis, how to arrive at the decision using formulated decision rule.
Students can use this solution as a model solution to work out other similar type of problems and it makes them easy to remember the steps and procedure involved in such type of problems.

Please help answer the following questions involving statistics.
1. Why do we use hypothesis testing?
2. What is a test statistic and how is it related to a critical value in hypothesis testing?
3. What is the critical region in hypothesis testing and why is it important?

Question :
The mean score on a standardized psychology test is supposed to be 50. Believing that a group of psychologists will score higher, we test a random sample of 11 psychologists. Their mean score is 45 with s=3. Test at a level of significance of 1%.

You have collected the following data from two suppliers. Are the suppliers significantly different at the 0.05 level of significance?
Supplier One Supplier TwoSample Size 45 52
Sample mean 8.1 9.3
Sa

1. We have now studied twostatistics Z and t. Compare and contrast the use of these two statistical tests, with particular attention to the quantity and quality of the data we use in each test. Is one test better than the other?
2. In research the concept of p value is useful to interpret the results of a hypothesis test.

Ho:u1-u2 = 0
Ha:u1-u2 does not equal 0
The following results are for two independent samples taken from the two populations.
Sample 1
N1 = 80
x1 = 104
o1 = 8.4
Sample 2
N2 = 70
x2 = 106
o2 = 7.6
1. What is the value of the test statistic?
2. What is the p-value
3. With a=.05, what is your co

1. Suppose you want to test the claim that the mean does not equal 3.5. Given a sample size of n = 31 and a level of significance of when should you reject H0 ?
a. Reject H0 if the standardized test statistic is greater than 2.33 or less than -2.33
b. Reject H0 if the standardized test statistic is greater than 1.645 or les

Use the given claim to state a null and an alternative hypothesis. Identify which hypothesis represents the claim.
A. Claim: p < 0.205
B. Claim: p > 0.70
Test the claim about the population mean ยต with a z-test using the given samplestatistics and l

An office equipment company advertises that it will deliver equipment within 15 days of purchase. A sample of 49 past deliveries is taken to test whether company's advertisement is valid. The delivery time for this sample was 16.2 days with a sample standard deviation of 5.6 days. Which of the following is correct
* What is t