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amid [387]
3 years ago
6

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 215 vinyl​ glov

es, 70​% leaked viruses. Among 215 latex​ gloves, 7​% leaked viruses.
1. Using a 0.01 significance​ level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves.
Mathematics
2 answers:
Marianna [84]3 years ago
7 0

Answer:

Step-by-step explanation:

Download docx
pickupchik [31]3 years ago
3 0

Answer:

z=\frac{0.7-0.07}{\sqrt{0.385(1-0.385)(\frac{1}{215}+\frac{1}{215})}}=13.42  

p_v =P(Z>13.42)\approx 0  

So the p value is a very low value and using any significance level given \alpha=0.01 we se that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that vinyl gloves have a greater virus leak rate than latex gloves at 1% of significance.

Step-by-step explanation:

Data given and notation  

n_{V}=215 sample of vinyl gloves selected

n_{L}=215 sample of latex gloves selected

p_{V}=0.7 represent the proportion of vynil gloves with leaked viruses

p_{L}=0.07 represent the proportion of latex gloves with leaked viruses

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the vinyl gloves have a greater virus leak rate than latex gloves , the system of hypothesis would be:  

Null hypothesis:p_{V} \leq p_{L}  

Alternative hypothesis:p_{V} > \mu_{L}  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{V}-p_{L}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{V}}+\frac{1}{n_{L}})}}   (1)

Where \hat p=\frac{X_{V}+X_{L}}{n_{V}+n_{L}}=\frac{0.7+0.07}{2}=0.385

Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.7-0.07}{\sqrt{0.385(1-0.385)(\frac{1}{215}+\frac{1}{215})}}=13.42  

Statistical decision

Since is a one right tailed test the p value would be:  

p_v =P(Z>13.42)\approx 0  

So the p value is a very low value and using any significance level given \alpha=0.01 we se that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that vinyl gloves have a greater virus leak rate than latex gloves at 1% of significance.

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