Setting the Alternative Hypothesis
The piston diameter of a certain hand pump is 0.6 inch. The manager determines that the diameters are normally distributed, with a mean of 0.6 inch and a standard deviation of 0.005 inch. After recalibrating the production machine, the manager randomly selects 21 pistons and determines that the standard deviation is 0.0033 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the $\alpha=0.10$ level of significance?
The alternative hypothesis is $\mathrm{H}_{1}$ :
Calculate the value of the test statistic.
$\chi^{2}=\square$ (Round to three decimal places as needed.)
Use technology to determine the P-value for the test statistic.
The P-value is
(Round to three decimal places as needed.)
What is the correct conclusion at the $\alpha=0.10$ level of significance?
Since the P-value is
than the level of significance,
the null hypothesis. There
sufficient evidence to conclude that the
standard deviation has decreased at the 0.10 level of significance.
Setting the Null Hypothesis
Identify the type I error and the type II error that corresponds to the given hypothesis.
The proportion of people who write with their left hand is equal to 0.33 .
Which of the following is a type II error?
A. Fail to reject the claim that the proportion of people who write with their left hand is 0.33 when the proportion is actually 0.33 .
B. Reject the claim that the proportion of people who write with their left hand is 0.33 when the proportion is actually different from 0.33 .
C. Reject the claim that the proportion of people who write with their left hand is 0.33 when the proportion is actually 0.33 .
D. Fail to reject the claim that the proportion of people who write with their left hand is 0.33 when the proportion is actually different from 0.33 .
Get more help .
Clear all
Check answer
Determining if Left, Right, or Two Tailed Test Given the Null Hypothesis
The test statistic of $z=2.88$ is obtained when testing the claim that $p>0.29$. This is a right-tailed test. Using a 0.01 significance level, complete parts (a) and (b).
Click here to view the standard normal distribution table for negative $z$ scores.
Click here to view the standard normal distribution table for positive $z$ scores.
b. Should we reject $\mathrm{H}_{0}$ or should we fail to reject $\mathrm{H}_{0}$ ?
A. $\mathrm{H}_{0}$ should not be rejected, since the test statistic is in the critical region.
B. $\mathrm{H}_{0}$ should not be rejected, since the test statistic is not in the critical region.
C. $\mathrm{H}_{0}$ should be rejected, since the test statistic is not in the critical region.
D. $\mathrm{H}_{0}$ should be rejected, since the test statistic is in the critical region.
Determining if Left, Right, or Two Tailed Test Given the Alternative Hypothesis
Use technology to find the P-value for the hypothesis test described below.
The claim is that for $12 \mathrm{AM}$ body temperatures, the mean is $\mu<98.6^{\circ} \mathrm{F}$. The sample size is $n=6$ and the test statistic is $\mathrm{t}=-1.979$.
P-value $=\square($ Round to three decimal places as needed. $)$