Researchers at Mississippi State University were studying the impact of different environmental sounds on ecosystems. For their
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Answer:
There is enough evidence to support the claim that the true proportion of monitors with dead pixels is greater than 5%.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 300
p = 5% = 0.05
Alpha, α = 0.05
Number of dead pixels , x = 24
First, we design the null and the alternate hypothesis
This is a one-tailed(right) test.
Formula:
Putting the values, we get,
Now, we calculate the p-value from excel.
P-value = 0.00856
Since the p-value is smaller than the significance level, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Conclusion:
Thus, there is enough evidence to support the claim that the true proportion of monitors with dead pixels is greater than 5%.
Answer:
95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].
Step-by-step explanation:
We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).
In the first stages of a clinical trial, it was successful for 7 out of the 14 women.
Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of women who find success with this new treatment =
= 0.50
n = sample of women = 14
<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>
So, 95% confidence interval for the true proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%
level of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( < p <
) = 0.95
<u />
<u>95% confidence interval for p</u> = [ ,
]
= [ ,
]
= [0.238 , 0.762]
Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].