Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \leq 25 } \\ { H _ { \mathrm { a } } : \mu > 25 } \end{array}$$

A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.

What is the rejection rule using the critical value? What is your conclusion?

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \geq 20 } \\ { H _ { \mathrm { a } } : \mu < 20 } \end{array}$$

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

Compute the value of the test statistic.

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \geq 20 } \\ { H _ { \mathrm { a } } : \mu < 20 } \end{array}$$

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

Using $\alpha$ = .05, what is your conclusion?

Consider the following hypothesis test :

$$\begin{align*} H_0 : &\ \mu \geq 20 \\ H_a :&\ \mu < 20 \end{align*}$$

A sample of $50$ provided a sample mean of $19.4$. The population standard deviation is $3$.

Compute the value of the test statistic (up to $2$ decimals).

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \geq 20 } \\ { H _ { \mathrm { a } } : \mu < 20 } \end{array}$$

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

What is the p-value?

Consider the following hypothesis test.

$$\begin{aligned} & H_0: \mu \geq 20 \\ & H_{\mathrm{a}}: \mu<20 \end{aligned}$$

A sample of $50$ provided a sample mean of $19.4$. The population standard deviation is $2$. State the critical values for the rejection rule.

$BusinessWeek$ conducted a survey of graduates from $30$ top MBA programs ($BusinessWeek,$ September $22, ~2003$). On the basis of the survey, assume that the mean annual salary for male and female graduates $10$ years after graduation is $\$168,000$ and $\$117,000$, respectively. Assume the standard deviation for the male graduates is $\$40,000$, and for the female graduates it is $\$25,000.$

What is the probability that a simple random sample of $40$ female graduates will provide a sample mean within $\$10,000$ of the population mean, $\$117,000$?

$BusinessWeek$ conducted a survey of graduates from $30$ top MBA programs ($BusinessWeek,$ September $22, ~2003$). On the basis of the survey, assume that the mean annual salary for male and female graduates $10$ years after graduation is $\$168,000$ and $\$117,000$, respectively. Assume the standard deviation for the male graduates is $\$40,000$, and for the female graduates it is $\$25,000.$

What is the probability that a simple random sample of $100$ male graduates will provide a sample mean more than $\$4000$ below the population mean?

$BusinessWeek$ conducted a survey of graduates from $30$ top MBA programs ($BusinessWeek,$ September $22, ~2003$). On the basis of the survey, assume that the mean annual salary for male and female graduates $10$ years after graduation is $\$168,000$ and $\$117,000$, respectively. Assume the standard deviation for the male graduates is $\$40,000$, and for the female graduates it is $\$25,000.$

What is the probability that a simple random sample of $40$ male graduates will provide a sample mean within $\$10,000$ of the population mean, $\$168,000$?

BusinessWeek conducted a survey of graduates from 30 top MBA programs (BusinessWeek, September 22, 2003). On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is 168,000 dollar and 117,000 dollars, respectively. Assume the standard deviation for the male graduates is 40,000 dollars, and for the female graduates it is 25,000 dollars. a. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within 10,000 dollar of the population mean, 168,000 dollars? $\newline$ b. What is the probability that a simple random sample of 40 female graduates will provide a sample mean within 10,000 dollars of the population mean, 117,000 dollars ?$\newline$ c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within 10,000 dollars of the population mean? Why?

Distinguish between *(a) the sample standard deviation and the population standard deviation. (b) the meaning of the word "sample" as it is used in a chemical and in a statistical sense.

Identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation ; (c) sample variance; (d) population variance.

Consider the following hypothesis test:

$$\begin{aligned} & H_0: \mu \leq 12 \\ & H_{\mathrm{a}}: \mu>12 \end{aligned}$$

A sample of 25 provided a sample mean $\bar{x}=14$ and a sample standard deviation $s=4.32$.

Compute the value of the test statistic.

Use the $t$ distribution table (Table 2 in Appendix B) to compute a range for the $p$-value.

At $\alpha=.05$, what is your conclusion?

What is the rejection rule using the critical value? What is your conclusion?

Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $\$220$ per hour. A research study will measure the cost of the new method over a sample production period.

Comment on the conclusion when $H _ { 0 }$ can be rejected.