91Ó°ÊÓ

No homework? Mr. Tabor believes that less than $75\%$of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of $50$ students at the school.

Mr. Tabor believes that less than $75\%$ of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of $50$ students at the school.

In the study of older students’ attitudes, the sample mean SSHA score was $125.7$and the sample standard deviation was $29.8$. A significance test yields a P-value of $0.0101$.

a. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.

Attitudes Refer to Exercise 4. In the study of older students’ attitudes, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101.

a. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.

Power calculation: potatoes Refer to Exercise 85.

a. Suppose that $H_0:p=0.08$is true. Describe the shape, center, and variability of the sampling distribution of $\hat{p}$ in random samples of size $500$

b. Use the sampling distribution from part (a) to find the value of $\hat{p}$with an area of $0.05$to the right of it. If the supervisor obtains a random sample of $500$potatoes with a sample proportion of defective potatoes greater than this value of p^, he will reject $H_0:p=0.08$at the $\mathrm{Î\pm }=0.05$significance level.

c. Now suppose that $p=0.11$Describe the shape, center, and variability of the sampling distribution of $\hat{p}$in random samples of size $500$

d. Use the sampling distribution from part (c) to find the probability of getting a sample proportion greater than the value you found in part (b). This result is the power of the test to detect $p=0.11$

The reason we use t procedures instead of $z$ procedures when carrying out a test about a population mean is that

a. z requires that the sample size be large.

b. z requires that you know the population standard deviation $\mathrm{σ}$

c. z requires that the data come from a random sample.

d. z requires that the population distribution be Normal.

e. z can only be used for proportions.

You are testing $H_0:\mathrm{μ}=10$against $H_a:\mathrm{μ}<10$based on an SRS of$20$

observations from a Normal population. The t statistic is $t=−2.25$

The $P-$value

a. falls between 0.01 and 0.02.

b. falls between 0.02 and 0.04.

c. falls between 0.04 and 0.05.

d. falls between 0.05 and 0.25.

e. is greater than 0.25.

You are testing $H_0:\mathrm{μ}=10$ against $H_a:\mathrm{μ}≠10$ based on an SRS of $15$

observations from a Normal population. What values of the t statistic are statistically significant at the $\mathrm{Î\pm }=0.005$ level?

After checking that conditions are met, you perform a significance test of $H_0:\mathrm{μ}=1$versus $H_a:\mathrm{μ}≠1$You obtain a $P-$value of $0.022$Which of the following must be true?

a. A $95\%$confidence interval for ${\mathrm{μ}}^{\mathrm{μ}}$ will include the value $1$

b. A $95\%$confidence interval for ${\mathrm{μ}}^{\mathrm{μ}}$ will include the value $0.022$

c. A $99\%$confidence interval for ${\mathrm{μ}}^{\mathrm{μ}}$ will include the value$1$

d. A $99\%$confidence interval for ${\mathrm{μ}}^{\mathrm{μ}}$ will include the value $0.022$

e. None of these is necessarily true.

The most important condition for making an inference about a population mean from a significance test is that

a. the data come from a random sample.

b. the population distribution is exactly Normal.

c. the data contain no outliers.

d. the sample size is less than $10\%$ of the population size.

e. the sample size is at least $30$