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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 9: Q T9.9 (page 616)

Bags of a certain brand of tortilla chips claim to have a net weight of $14$ ounces. 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
$H_{0} : μ = 14 H_{a} : μ < 14$
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

$H_{0} : μ = 14$

$H_{1} : μ < 14$

02

Step 2:Explaination

Type I error: Reject the null hypothesis $H_{0}$ , once the null hypothesis $H_{0}$ 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

How much juice? One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of $180$ milliliters (ml) of liquid. A quality-control inspector must check that the machine is working properly. The inspector takes a random sample of $40$ bottles and measures the volume of liquid in each bottle.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

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 $H 0 : p > 0.37 H_{0} : p > 0.37$ is tested against the alternative Ha: $p = 0.37 H_{a} : p = 0.37$

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

$H0: x^{-} = 3000 {grams}^{- 5} H_{0} : \bar{x} = 3000 grams$

Ha: $x^{-} < 3000$ grams $H_{a} : \bar{x} < 3000$ grams

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

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $\(85, 000$ to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of $50$ people living near one potential site. Based on the mean income of this sample, you will perform a test at the

$α = 0.05$ significance level of $H_{0} : μ = \) 85, 000$ versus $H_{a} : μ > \(85, 000$ , where $μ$ is the true mean income in the population of people who live near the restaurant. The power of the test to detect that $μ = \) 86, 000$ is $0.64$ Interpret this value.

Based on the $P$ -value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject $H_{0}$ . We have convincing evidence that more than $50 %$ of city residents support the tax increase.

b. Because the $P$ -value is large, we fail to reject $H_{0}$ . We have convincing evidence that more than $50 %$ of city residents support the tax increase.

c. Because the $P$ -value is large, we reject $H_{0}$ . We have convincing evidence that at most $50 %$ of city residents support the tax increase.

d. Because the $P$ -value is large, we fail to reject $H_{0}$ . We have convincing evidence that at most $50 %$ of city residents support the tax increase.

e. Because the $P$ -value is large, we fail to reject $H_{0}$ . We do not have convincing

evidence that more than $50 %$ of city residents support the tax increase.

We want to be rich In a recent year, $73 %$ of first-year college students responding to a national survey identified “being very well-off financially” as an important personal goal. A state university finds that $132$ of an SRS of $200$ of its first-year students say that this goal is important. Is there convincing evidence at the $α = 0.05$ significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value of 73%?

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