The average annual salary of an administrative assistant in Massachusetts was $3
ID: 3127317 • Letter: T
Question
The average annual salary of an administrative assistant in Massachusetts was $36,956 in 2010. Imagine that a social scientist randomly selected 400 administrative assistants and asked their salary. He obtained the mean salary was $36,500 and the sample standard deviation was 500. What's the lower limit for the 95% of the confidence interval of the mean? A researcher wanted to know the percentage of the urban population that had ever experienced depression in the past month. He randomly sampled 500 adults in a big city. He found that 20 percent of them had experienced any type of depression in the past month. What is the upper limit of 95% of the confidence interval (as proportion)? For a standard normal distribution, what is the probability of getting a positive number? For a normal distribution with a mean of 3 and standard deviation of 2, what is the probability of getting a number greater than 5?Explanation / Answer
2.
Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 36500
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 500
n = sample size = 400
Thus,
Lower bound = 36458.87866 [ANSWER]
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