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Math  /  Data & Statistics

QuestionA newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 281 vinyl gloves, 70%70 \% leaked viruses. Among 281 latex gloves, 6%6 \% leaked viruses. Using the accompanying display of the technology results, and using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1.
What are the null and alternative hypotheses? A. H0:P1<P2H_{0}: P_{1}<P_{2} H1:p1=p2H_{1}: p_{1}=p_{2} D. H0:p1=p2H_{0}: p_{1}=p_{2} H1:p1≠p2H_{1}: p_{1} \neq p_{2} B. H0:p1=p2H_{0}: p_{1}=p_{2} C. H0:p1>p2H_{0}: p_{1}>p_{2} H1:p1>p2H_{1}: p_{1}>p_{2} H1:p1=p2H_{1}: p_{1}=p_{2} E. H0:p1=p2H_{0}: p_{1}=p_{2} F. H0:p1≠p2H_{0}: p_{1} \neq p_{2} H1:p1<p2H_{1}: p_{1}<p_{2}
Identify the test statistic. 15.64 (Round to two decimal places as needed.) Identify the P -value. □\square (Round to three decimal places as needed.)

Studdy Solution

STEP 1

1. We are comparing the proportions of virus leakage between two types of gloves: vinyl (population 1) and latex (population 2).
2. The significance level for the hypothesis test is α=0.10 \alpha = 0.10 .
3. The null hypothesis assumes no difference in leakage rates, while the alternative hypothesis suggests a greater leakage rate for vinyl gloves.

STEP 2

1. Define the null and alternative hypotheses.
2. Calculate the test statistic.
3. Determine the P-value.
4. Make a decision based on the P-value and significance level.

STEP 3

Define the null and alternative hypotheses.
- Null Hypothesis (H0H_0): The proportions of virus leakage are equal for both types of gloves. - Alternative Hypothesis (H1H_1): The proportion of virus leakage is greater for vinyl gloves than for latex gloves.
The correct choice is:
H0:p1=p2 H_0: p_1 = p_2 H1:p1>p2 H_1: p_1 > p_2

STEP 4

Calculate the test statistic.
Given the test statistic is provided as:
15.64 15.64

STEP 5

Identify the P-value.
To find the P-value, we would typically use the test statistic in conjunction with a standard normal distribution table or a statistical software. However, since the P-value is not provided, it needs to be calculated or obtained from the technology results.
P-value=□ \text{P-value} = \square

STEP 6

Make a decision based on the P-value and significance level.
- If the P-value is less than α=0.10 \alpha = 0.10 , reject the null hypothesis. - If the P-value is greater than or equal to α=0.10 \alpha = 0.10 , fail to reject the null hypothesis.
Please calculate or provide the P-value to proceed with the decision-making step.

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