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Chapter 9: Q. 66. (page 606)

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.

Short Answer

Expert verified

The required answer is:

Yes, the conditions are fulfilled.

Step by step solution

01

Given information

Hypothesized population mean 渭0=19.2

Sample size (n)=75

Level of significance (伪)=0.10

The null and alternative hypotheses are as follows:

H0:渭=19.2Ha:渭notequalto19.2

02

The objective is to check whether the conditions required to perform the hypothesis test for the population mean are satisfied or not.

The following conditions must be met before conducting a hypothesis test on 渭:

Simple random samples must be drawn from the population.

The sample size should be large, n>30or the population should be normally distributed.

Requirement check:

The sample of 75candy bags is assumed to be chosen at random.

The sample size exceeds 30

Therefore, both the required conditions are met.

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Most popular questions from this chapter

18%Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1%increase in the sales tax to fund road repairs.

In the sample, p^=158/300=0.527, The resulting P-value is 0.18. What is the correct interpretation of this P-value?

a. Only 18% of the city residents support the tax increase.

b. There is an 18%chance that the majority of residents supports the tax increase.

c. Assuming that 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

d. Assuming that more than 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

e. Assuming that 50%of residents support the tax increase, there is an 18% chance that the null hypothesis is true by chance alone.

The standardized test statistic for a test of H0:p=0.4versus Ha:pnotequalto0.4isz=2.43This 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 p^

You are testing H0:渭=10 against Ha:渭鈮�10 based on an SRS of 15

observations from a Normal population. What values of the t statistic are statistically significant at the 伪=0.005 level?

a.t>3.326b.t>3.286c.t>2.977d.t<鈭�3.326ort>3.326e.t<鈭�3.286ort>3.286

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?

Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.

a. State appropriate hypotheses for testing the company鈥檚 claim. Be sure to define your parameter.

b. Describe a Type I error and a Type II error in this setting, and give the consequences Page Number: 615 of each.

c. Would you recommend a significance level of 0.01, 0.05, or 0.10 for this test? Justify your choice.

d. The power of the test to detect the fact that only 3% of adults who use this vaccine would develop flu using 伪=0.05 is 0.9437. Interpret this value.

e. Explain two ways that you could increase the power of the test from part (d).
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