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Answer:
a) Parameter of interest representing the true proportion of the plates have blistered.
b) Null hypothesis:
Alternative hypothesis:
c)
d) For this case we need to find a value in the normal standard distribution that accumulates 0.1 of the area in the right tail and for this case is:
e) For this case since our calculated value is higher than the critical value 1.33>1.28 we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly higher than 0.1
f)
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the true proportion is higher than 0.1 or 10%
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
Part a
Parameter of interest representing the true proportion of the plates have blistered.
X=14 represent the number of the plates have blistered.
estimated proportion of the plates have blistered.
is the value that we want to test
represent the significance level
Confidence=90% or 0.90
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Part b: Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that more than 10% of all plates blister under such circumstances.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Part c: Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Part d: Rejection region
For this case we need to find a value in the normal standard distribution that accumulates 0.1 of the area in the right tail and for this case is:
Part e
For this case since our calculated value is higher than the critical value 1.33>1.28 we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly higher than 0.1
Part f
Since is a right taild test the p value would be:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the true proportion is higher than 0.1 or 10%