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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

Candy! A machine is supposed to fill bags with an average of 19.2 ounces of candy. The manager of the candy factory wants to be sure that the machine does not consistently underfill or overfill the bags. So the manager plans to conduct a significance test at the 伪=0.10significance level of

H0:渭=19.2Ha:渭notequalto19.2

where 渭=the true mean amount of candy (in ounces) that the machine put in all bags filled that day. The manager takes a random sample of 75 bags of candy produced that day and weighs each bag. Check if the conditions for performing the test are met.

Which of the following 95%confidence intervals would lead us to reject H0:p=0.30in favor of Ha:pnotequalto0.30at the 5%significance level?

a. (0.19,0.27)

b.(0.24,0.30)

c. (0.27,0.31)

d. (0.29,0.31)

e. None of these

Making conclusions A student performs a test of H0:p=0.75versus Ha:p<0.75at 伪=0.05significance level and gets a P-value of 0.22

The student writes: 鈥淏ecause the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Which of the following has the greatest probability?

a.P(t>2)if t has 5 degrees of freedom.

b. P(t>2) if t has 2 degrees of freedom.

c. P(z>2) if z is a standard Normal random variable.

d.P(t<2)if t has 5 degrees of freedom.

e.P(z<2) if z is a standard Normal random variable.

Don鈥檛 argue Refer to Exercises 2 and 12.

a. What conclusion would you make at the 伪=0.01 level?

b. Would your conclusion from part (a) change if a 5% significance level was used

instead? Explain your reasoning.
See all solutions

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