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Chapter 9: Q.79 (page 589)

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=11.5. The hardness data for a random sample of 20 tablets are

11.627 11.613 11.493 11.602 11.360

11.374 11.592 11.458 11.552 11.463

11.383 11.715 11.485 11.509 11.429

11.477 11.570 11.623 11.472 11.531

Is there significant evidence at the 5% level that the mean hardness of the tablets differs from the target value? Carry out an appropriate test to support your answer.

Short Answer

Expert verified

the mean hardness of the tablets does not differ from the target value.

Step by step solution

01

Given Information

The hardness data for a random sample of 20tablets are

11.627鈥呪赌呪赌呪赌�11.613鈥呪赌呪赌呪赌�11.493鈥呪赌呪赌呪赌�11.602鈥呪赌呪赌呪赌�11.36011.374鈥呪赌呪赌呪赌�11.592鈥呪赌呪赌呪赌�11.458鈥呪赌呪赌呪赌�11.552鈥呪赌呪赌呪赌�11.46311.383鈥呪赌呪赌呪赌�11.715鈥呪赌呪赌呪赌�11.485鈥呪赌呪赌呪赌�11.509鈥呪赌呪赌呪赌�11.42911.477鈥呪赌呪赌呪赌�11.570鈥呪赌呪赌呪赌�11.623鈥呪赌呪赌呪赌�11.472鈥呪赌呪赌呪赌�11.531
02

Explanation

From the data given,

x-=11.516

渭=11.5

we calculate the null and alternative hypotheses,

H0:渭=11.5Ha:渭鈮�11.5

Using,

localid="1652942386796" t=x-鈭�渭sn=11.516鈭�11.500.095020=0.77

The test statistic =0.77

Hence the mean hardness of the tablets does not differ from the target value 渭=11.5as the critical value2.093 is greater than the test statistic 0.77.

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Most popular questions from this chapter

Roulette an American roulette wheel has 18red slots among its 38slots.In a random sample of 50pins,the ball lands in a red slot 31times.

(a) Do the data give convincing evidence that the wheel is unfair? Carry out an appropriate test at the伪=0.05significance level to help answer this question.

(b) The casino manager uses your data to produce a 99%confidence interval for pand gets role="math" localid="1650358305073" 0.44,0.80. He says that this interval provides convincing evidence that the wheel is fair. How do you respond?

- If conditions are met, conduct a one-sample \(t\) test about a population mean \(\mu\).

The z statistic for a test of H0 :p = 0.4 versus Ha : p > 0.4 is z = 2.43. This test is

(a) not significant at either 伪=0.05or 伪=0.01.

(b) significant at 伪=0.05but not at 伪=0.01

(c) significant at 伪=0.01but not at 伪=0.05.

(d) significant at both 伪=0.05and 伪=0.01.

(e) inconclusive because we don鈥檛 know the value of 藛p .

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=11.5. The hardness data for a random sample of 20tablets are

11.62711.61311.49311.60211.36011.37411.59211.45811.55211.46311.38311.71511.48511.50911.42911.47711.57011.62311.47211.531

Is there significant evidence at the5% level that the mean hardness of the tablets differs from the target value? Carry out an appropriate support your answer.

Are TV commercials louder than their surrounding programs? To find out, researchers collected data on 50randomly selected commercials in a given week. With the television鈥檚 volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first 30seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is

(a) a one-proportion z test.

(b) a one-proportion z interval.

(c) a paired t test.

The reason we use tprocedures instead of zprocedures when carrying out a test about a population mean is that

(a) zcan be used only for large samples.

(b)zrequires that you know the population standard deviation 蟽.

(c) zrequires you to regard your data as an SRS from the population.

(d) zapplies only if the population distribution is perfectly Normal.

(e) zcan be used only for confidence intervals.
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