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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

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is 179.6ml and the standard deviation is 1.3ml. A significance test yields a P-value of 0.0589. Interpret the P-value.

Fair coin? You want to determine if a coin is fair. So you toss it 10times and record the proportion of tosses that land 鈥渉eads.鈥� You would like to perform a test of H0:p=0.5versus Ha:p鈮�0.5, where p= the proportion of all tosses of the

coin that would land 鈥渉eads.鈥� Check if the conditions for performing the significance test are met.

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at a local high school. Before the change, 37%of students approve of the parking that's provided. The null hypothesis H0:p>0.37H0:p>0.37is tested against the alternative Ha: p=0.37Ha:p=0.37

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

H0:x-=3000grams-5H0:x炉=3000grams

Ha: x-<3000grams Ha:x炉<3000grams

explain what's wrong with the stated hypotheses. Then give correct hypotheses.

Roulette An American roulette wheel has 18red slots among its 38slots. To test if a particular roulette wheel is fair, you spin the wheel 50times and the ball lands in a red slot 31times. The resulting P-value is0.0384.

a. Interpret the P-value.

b. What conclusion would you make at the伪=0.05 level?

c. The casino manager uses your data to produce a99% confidence interval for p and gets(0.44,0.80). He says that this interval provides convincing evidence that the wheel is fair. How do you respond

Calculations and conclusions Refer to Exercise R9.1. Find the standardized test statistic and P-value in each setting, and make an appropriate conclusion.
See all solutions

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