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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

Bullies in middle school A media report claims that more than 75%of

middle school students engage in bullying behavior. A University of Illinois study on aggressive behavior surveyed a random sample of 558middle school students. When asked to describe their behavior in the last 30days, 445students admitted that they had engaged in physical aggression, social ridicule, teasing, name-calling, and issuing threats 鈥攁ll of which would be classified as bullying. Do these data provide convincing evidence at the 伪=0.05significance level that the media report鈥檚 claim is correct?

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay \)100 for the upgrade.

a. Do the sample data give convincing evidence that more than 20% of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the 伪=0.05significance level.

b. Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.

c. Suppose that 30% of the company鈥檚 customers would be willing to pay $100 for the upgrade. The power of the test to detect this fact is0.60. Interpret this value.

Flu vaccine Refer to ExerciseR9.5. Of the 1000 adults who were given the vaccine, 43 got the flu. Do these data provide convincing evidence to support the company鈥檚 claim?

Teen drivers Refer to Exercise 51.

a. Construct and interpret a 95% confidence interval for the true proportion p of all teens in the state who passed their driving test on the first attempt. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) provides more information than the test in Exercise 51.

Two-sided test Suppose you want to perform a test of H0:渭=64

versus Ha:渭notequalto64at the 伪=0.05significance level. A random sample

of size n=25 from the population of interest yields x炉=62.8 and sx=5.36

. Assume that the conditions for carrying out the test are met.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.
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