Which expression is equivalent to 144 Superscript three-halves? 216 1,728 RootIndex 3 StartRoot 12 EndRoot RootIndex 3 StartRoot
2 answers:
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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:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
For this case we select a sample of n =100
From the central limit theorem we know that the distribution for the sample mean is given by:
So then the sample mean would be:
And the standard deviation would be: