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A random sample of  n1 = 49  measurements from a population with population standard deviation  ?1 = 3  had a sample mean of  x1 = 9.  An independent random sample of  n2 = 64  measurements from a second population with population standard deviation  ?2 = 4  had a sample mean of  x2 = 11.  Test the claim that the population means are different. Use level of

- September 18, 2022 - Edwin Tunner

A random sample of 

n1 = 49

 measurements from a population with population standard deviation 

?1 = 3

 had a sample mean of 

x1 = 9.

 An independent random sample of 

n2 = 64

 measurements from a second population with population standard deviation 

?2 = 4

 had a sample mean of 

x2 = 11.

 Test the claim that the population means are different. Use level of significance 0.01.

(a) Check Requirements: What distribution does the sample test statistic follow? Explain.

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student’s t. We assume that both population distributions are approximately normal with unknown standard deviations.    The Student’s t. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

(b) State the hypotheses.

H0: ?1 = ?2; H1: ?1 < ?2H0: ?1 = ?2; H1: ?1 > ?2    H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 ≠ ?2; H1: ?1 = ?2

(c) Compute 

x1 − x2.

x1 − x2 = 

Compute the corresponding sample distribution value. (Test the difference ?1 − ?2. Round your answer to two decimal places.)

(d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

(e) Conclude the test.

At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.    At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(f) Interpret the results.

Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.    Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.
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