Answer:
So the p value is a very low value and using any significance level given we se that
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
sample of vinyl gloves selected
sample of latex gloves selected
represent the proportion of vynil gloves with leaked viruses
represent the proportion of latex gloves with leaked viruses
z would represent the statistic (variable of interest)
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:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
Since is a one right tailed test the p value would be:
So the p value is a very low value and using any significance level given we se that
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.