A random sample of

_{1}= 49

measurements from a population with population standard deviation

_{1}= 3

had a sample mean of

_{1}= 9.

An independent random sample of

_{2}= 64

measurements from a second population with population standard deviation

_{2}= 4

had a sample mean of

_{2}= 11.

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

*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.

*H*

_{0}: ?

_{1}= ?

_{2};

*H*

_{1}: ?

_{1}< ?

_{2}

*H*

_{0}: ?

_{1}= ?

_{2};

*H*

_{1}: ?

_{1}> ?

_{2}

*H*

_{0}: ?

_{1}= ?

_{2};

*H*

_{1}: ?

_{1}≠ ?

_{2}

*H*

_{0}: ?

_{1}≠ ?

_{2};

*H*

_{1}: ?

_{1}= ?

_{2}

(c) Compute

_{1}− x

_{2}.

_{1}− x

_{2}=

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.

(f) Interpret the results.