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 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.

$H_0:$ $mu equals 100 comma 000$

$H_{a}:$ $mu is greater than 100 comma 000$

$H_0:$ $mu equals 100 comma 000$

$H_{a}:$ $mu is not equal to 100 comma 000$

$H_0:$ $\mu=100,000$

$H_{a}:$ $μ$ < $100 comma 000$

$H_0:$ $\mu\ne100,000$

$H_{a}:$ $\mu=100,000$

Verified step by step guidance

Understand the context: The theme park claims their weekly attendance is 100,000. You suspect it is different, which suggests a two-tailed test.

Define the null hypothesis (H0): The null hypothesis represents the status quo or the claim being tested. In this case, H0: μ = 100,000, where μ is the population mean of weekly attendance.

Define the alternative hypothesis (Ha): The alternative hypothesis represents the claim you are testing against the null hypothesis. Since you believe the attendance is different, Ha: μ ≠ 100,000.

Recognize the type of test: Since the alternative hypothesis is not equal (≠), this is a two-tailed test, which checks for any significant difference from the claimed value.

Consider the implications: If the sample data provides enough evidence to reject the null hypothesis, it suggests the true mean attendance is significantly different from 100,000.

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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.

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tTest The bag of Hershey’s Kisses includes 75 of the candies. According to the label, the total weight is 340 g, so the candies should have a mean weight of 340/75 = 4.5333 g. Use the sample of weights listed above to test the claim that they are from a population with a mean of 4.5333 g. Use a 0.05 significance level with a t test. What does the conclusion suggest about the claim of 340 g printed on the label?

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 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.

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.

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Struggling with Statistics?

A popular theme park claims that their weekly attendance is around 100,000100,000. You believe that the weekly attendance is different than this claimed value, so you gather sample data. Write the null and alternative hypotheses.

Watch next

Steps in Hypothesis Testing practice set

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.