9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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Multiple Choice

A candy manufacturer seeking to minimize the variation in weights of their candies claims to produce candies with a standard deviation less than $0.300$ g. Write the null and alternative hypotheses.

$H_0:$ $sigma equals 0.300$ g

$H_{a}:$ $sigma is greater than 0.300$ g

$H_0:$ $\sigma=0.300$ g

$H_{a}:$ $sigma is not equal to 0.300$ g

$H_0:$ $\sigma=0.300$ g

$H_{a}:$ $σ$ < $0.300$ g

$H_0:$ $\sigma>0.300$ g

$H_{a}:$ $\sigma$ < $0.300$ g

Verified step by step guidance

Identify the parameter of interest, which is the standard deviation (σ) of the candy weights.

Understand that the manufacturer claims the standard deviation is less than 0.300 g, indicating a one-tailed test.

Formulate the null hypothesis (H0) as the statement that the standard deviation is equal to 0.300 g, i.e., H0: σ = 0.300 g.

Formulate the alternative hypothesis (Ha) as the statement that the standard deviation is less than 0.300 g, i.e., Ha: σ < 0.300 g.

Recognize that the null hypothesis represents the status quo or the claim to be tested, while the alternative hypothesis represents the claim the manufacturer is making.

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Related Practice

Textbook Question

In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

Sign Test Repeat Exercise 3 using the sign test to test the claim that the sample of weights is from a population with a median of 4.5333 g.

Textbook Question

In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

Wilcoxon Signed-Ranks Test Repeat Exercise 3 using the Wilcoxon signed-ranks test to test the claim that the sample of weights is from a population with a median of 4.5333 g.

Textbook Question

In Exercises 1–10, use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.

World Series The last 114 baseball World Series ended with 66 wins by American League teams and 48 wins by National League teams. Use the sign test to test the claim that in each World Series, the American League team has a 0.5 probability of winning.

Multiple Choice

A popular theme park claims that their weekly attendance is around $100 comma 000$ . You believe that the weekly attendance is different than this claimed value, so you gather sample data. Write the null and alternative hypotheses.

Multiple Choice

A survey claimed that $30 percent sign$ of adults prefer electric cars over traditional cars. A car manufacturer believes the true proportion is higher than $30 percent sign$ . To test this, they survey a random sample of $50$ adults and find that $19$ say they prefer electric cars. Determine which test statistic to use & calculate it.

Multiple Choice

Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

$H sub 0 colon$ $p equals 0.4$

$H_{a} :$ $p is not equal to 0.4$

Multiple Choice

In a certain hypothesis test, $H sub 0 colon p equals 0.4$ , $H_{a} : p$ < $0.4$ . You collect a sample and calculate a test statistic $z = - 1.32$ . Find the $P$ -value.

Textbook Question

Stem Cell Survey In a Newsweek poll of 882 adults, 481 (or 55%) said that they were in favor of using federal tax money to fund medical research using stem cells obtained from human embryos. A politician claims that people don’t really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Use the following probabilities related to determining whether the result of 481 is significantly high (assuming the true rate is 50%). Is 481 significantly high? What should be concluded about the politician’s claim? Explain.

P(respondent says to use the federal tax money) = 0.5

P(among 882, exactly 481 says to use federal tax money) = 0.000713

P(among 882,481 or more say to use federal tax money) = 0.00389

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Struggling with Statistics?

A candy manufacturer seeking to minimize the variation in weights of their candies claims to produce candies with a standard deviation less than 0.3000.300 g. Write the null and alternative hypotheses.

Watch next

Steps in Hypothesis Testing practice set

A candy manufacturer seeking to minimize the variation in weights of their candies claims to produce candies with a standard deviation less than $0.300$ g. Write the null and alternative hypotheses.