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Chapter 9: Q. 77. (page 607)

Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is 渭=11.5The hardness data for a random sample of 20 tablets from one large batch are

Is there convincing evidence at the 5%level that the mean hardness of the tablets in this batch differs from the target value?

Short Answer

Expert verified

No, there is sufficient evidence to show that the mean hardness is different from the targeted value.

Step by step solution

01

Given information

The data set is:

02

The objective is to find whether there is sufficient evidence to show that the mean hardness is different from the targeted value of 11.5at 5%the significance level.

We know,

The test statistic formula is: t=x炉-渭osn

The null and alternative hypotheses are as follows:

H0:渭=11.5Ha:渭notequalto11.5

The alternative hypothesis denotes a two-tailed test.

The Minitab output is as follows:

The p-value is 0.449

Here, p-value (0.449)>伪(0.05)The null hypothesis does not fail.

There is insufficient evidence at the 5%level of significance to show that the mean hardness of the tablets differs from the target value of11.5.

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Most popular questions from this chapter

Tests and confidence intervals The P-value for a two-sided test of the null hypothesis H0:渭=15is0.03

a. Does the 99% confidence interval for 渭 include 15? Why or why not?

b. Does the 95% confidence interval for 渭 include 15? Why or why not?

How much juice? One company鈥檚 bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. The company has been getting negative feedback from customers about underfilled bottles. To investigate, a quality-control inspector takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. Do these data provide convincing evidence at the伪=0.05significance level that the machine is underfilling the bottles?

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to 伪=0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11

Proposition XA political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of 1000registered voters, 482favor the proposition. Explain why it isn鈥檛 necessary to carry out a significance test in this setting.

Jump around Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was 15 inches. They wondered if the average vertical jump of students at their school differed from 15 inches, so they obtained a list of student names and selected a random sample of 20 students. After contacting these students several times, they finally convinced them to allow their vertical jumps to be measured. Here are the data (in inches):

Do these data provide convincing evidence at the 伪=0.10 level that the average vertical jump of students at this school differs from 15 inches?
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