9. Hypothesis Testing for One Sample

Performing Hypothesis Tests: Proportions

9. Hypothesis Testing for One Sample

Performing Hypothesis Tests: Proportions

Struggling with Statistics?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:
$alpha equals 0.10$ , $n equals 100$ , $x equals 42$ , & claim is $p equals 0.25$

Because $P$ -value = 0.00004 < $\alpha=$ 0.01, we FAIL TO REJECT $H_0$ . There is NOT ENOUGH evidence to suggest $H_{a}$ : $p$ ≠ 0.75

Because $P$ -value = 0.00004 < $\alpha=$ 0.01, we REJECT $H_0$ . There is ENOUGH evidence to suggest $H_{a}$ : $p$ ≠ 0.75

Because $P$ -value = 0.00008 < $\alpha=$ 0.01, we REJECT $H_0$ . There is ENOUGH evidence to suggest $H_{a}$ : $p$ ≠ 0.75

Because $P$ -value = 0.00008 < $\alpha=$ 0.01, we FAIL TO REJECT $H_0$ . There is NOT ENOUGH evidence to suggest $H_{a}$ : $p$ ≠ 0.75

Verified step by step guidance

Step 1: Define the null hypothesis (H₀) and the alternative hypothesis (Hₐ). The null hypothesis is H₀: p = 0.25, and the alternative hypothesis is Hₐ: p ≠ 0.25, since this is a two-tailed test.

Step 2: Calculate the sample proportion (p̂). The formula for p̂ is p̂ = x / n, where x is the number of successes (42) and n is the sample size (100).

Step 3: Verify the conditions for performing a hypothesis test for proportions. Ensure that both np and nq are greater than or equal to 5, where q = 1 - p. For np, calculate np = n * p, and for nq, calculate nq = n * q.

Step 4: Compute the test statistic (z-value). The formula for the z-value is z = (p̂ - p) / √(p * q / n), where p̂ is the sample proportion, p is the claimed proportion, q = 1 - p, and n is the sample size.

Step 5: Compare the calculated z-value to the critical z-value for α = 0.10 (two-tailed test) or use the p-value approach. If the p-value is less than α, reject the null hypothesis; otherwise, fail to reject the null hypothesis.

5:52m

Watch next

Master Performing Hypothesis Tests: Proportions with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

Lightning Deaths The graph in Cumulative Review Exercise 5 was created by using data consisting of 242 male deaths from lightning strikes and 64 female deaths from lightning strikes. Assume that these data are randomly selected lightning deaths and proceed to test the claim that the proportion of male deaths is greater than . Use a 0.01 significance level. Any explanation for the result?

views

Textbook Question

In Exercises 1–10, based on the nature of the given data, do the following:

a. Pose a key question that is relevant to the given data.

b. Identify a procedure or tool from this chapter or the preceding chapters to address the key question from part (a).

c. Analyze the data and state a conclusion.

Video Games In a survey of subjects aged 18–29, subjects were asked if they play video games often or sometimes. Among 1017 males, 72% answered “yes.” Among 984 females, 49% answered “yes” (based on data from a Pew Research Center survey).

views

Textbook Question

In Exercises 1–10, based on the nature of the given data, do the following:

a. Pose a key question that is relevant to the given data.

b. Identify a procedure or tool from this chapter or the preceding chapters to address the key question from part (a).

c. Analyze the data and state a conclusion.

Video Games In a survey of subjects aged 18–29, subjects were asked if they play video games often or sometimes. Among 984 females, 49% answered “yes” (based on data from a Pew Research Center survey).

views

Multiple Choice

Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:

$alpha equals 0.01$ , $n equals 40$ , $x equals 28$ , & claim is $p equals 0.75$

views

Multiple Choice

A local park claims that less than 15% of visitors litter. A random sample of 120 visitors finds that 25 litter. At the 0.05 significance level, test if the proportion of visitors who litter is greater than 15%.

views

Textbook Question

Feeling Your Age A research organization conducts a survey by randomly selecting adults and asking each, “How do you feel relative to your age?” The results are shown in the figure. (Adapted from Pew Research Center)

[IMAGE]

a. Use a sign test to test the null hypothesis that the proportion of adults who feel older is equal to the proportion of adults who feel younger. Assign a + sign to each adult who responded “older,” assign a - sign to each adult who responded “younger,” and assign a 0 to each adult who responded “my age.” Use α = 0.05

views

Textbook Question

Contacting Parents A research organization conducts a survey by randomly selecting adults and asking each, “How frequently do you contact your parents by phone?” The results are shown in the figure. (Adapted from Pew Research Center)

a. Use a sign test to test the null hypothesis that the proportion of adults who contact their parents by phone weekly is equal to the proportion of adults who contact their parents by phone daily. Assign a + sign to each adult who responded “weekly,” assign a - sign to each adult who responded “daily,” and assign a 0 to each adult who responded “other.” Use α = 0.05

views

Textbook Question

Explain how to test a population proportion p.

views

Show more practices

Performing Hypothesis Tests: Proportions practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice

Struggling with Statistics?

Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:α=0.10α=0.10, n=100n=100, x=42x=42, & claim is p=0.25p=0.25

Watch next

Performing Hypothesis Tests: Proportions practice set

Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:
$alpha equals 0.10$ , $n equals 100$ , $x equals 42$ , & claim is $p equals 0.25$