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Chapter 9: Q T9.9 (page 616)

Bags of a certain brand of tortilla chips claim to have a net weight of 14ounces. Net weights vary slightly from bag to bag and are Normally distributed with mean μ . A representative of a consumer advocacy group wishes to see if there is convincing evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H0:μ=14Ha:μ<14

A Type I error in this situation would mean concluding that the bags

a. are being underfilled when they aren’t.

b. are being underfilled when they are.

c. are not being underfilled when they are.

d. are not being underfilled when they aren’t.

e. are being overfilled when they are underfilled

Short Answer

Expert verified

opton a) are being underfilled when they aren’t.

Step by step solution

01

Step 1:Given information

H0:μ=14

H1:μ<14

02

Step 2:Explaination

Type I error: Reject the null hypothesisH0, once the null hypothesis H0 is true.

A type I error then associate with concluding that the bags are under filled, when type actually are not under filled

Therefore, the correct option is (a)

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Most popular questions from this chapter

Interpreting a P-value A student performs a test of H0:μ=100H0:μ=100versus Ha: μ>100Ha:μ>100and gets a P-value of 0.044.The student says, "There is a0.044 probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.

A milk processor monitors the number of bacteria per milliliter in raw milk received at the factory. A random sample of 10one-milliliter specimens of milk supplied by one producer gives the following data:

Construct and interpret a 90% confidence interval for the population mean μ.

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p≠0.25. Which of the following is an appropriate conclusion for them to draw at the α=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

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

coin that would land “heads.” Check if the conditions for performing the significance test are met.

Error probabilities and power You read that a significance test at the α=0.01

significance level has probability 0.14of making a Type II error when a specific alternative is true.

a. What is the power of the test against this alternative?

b. What’s the probability of making a Type I error?
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