Can someone give me simple formulas for the below problems. What I found is too confusing.
A sample of 145 values is randomly selected from a population with mean, ì, equal to 45 and standard deviation, ó, equal to 23. (Give your answers correct to one decimal place.)
(a) Determine the interval (smallest value to largest value) within which you would expect 99.7% of such sample means to lie.
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(b) What is the amount of deviation from the mean for a sample mean of 50?
(c) What is the maximum deviation you have allowed for in your answer to part (a)?
a) 99.7% = mean ± 2.96 SEm
SEm = SD/√n
b) SEm = SD/√n
c) See a.
thanks for the above but it still does not work out for me 45+2.96=47.96, 45-2.96=42.04 I don't think I understand this one
(a) To determine the interval within which you would expect 99.7% of the sample means to lie, you can use the formula:
Interval = ± (z-score) * (standard deviation / √sample size)
The z-score represents the number of standard deviations away from the mean. In this case, we want to find the interval containing 99.7% of the sample means, which corresponds to three standard deviations away from the mean. The z-score for a 99.7% confidence level is 3.
Substituting the given values into the formula:
Interval = ± (3) * (23 / √145)
Calculating this expression will give you the interval.
(b) To determine the amount of deviation from the mean for a sample mean of 50, you can subtract the mean from the sample mean:
Deviation = Sample Mean - Mean
Substituting the given values into the formula:
Deviation = 50 - 45
Calculating this expression will give you the amount of deviation from the mean.
(c) The maximum deviation allowed in the answer to part (a) is half of the interval width. Since the interval is expressed as ± (z-score) * (standard deviation / √sample size), the maximum deviation would be half of the interval width.
Interval Width = (2 * z-score) * (standard deviation / √sample size)
Substituting the given values into the formula:
Interval Width = (2 * 3) * (23 / √145)
Calculating this expression will give you the interval width. To find the maximum deviation, you divide the interval width by 2.
Maximum Deviation = Interval Width / 2
Calculating this expression will give you the maximum deviation allowed in the answer to part (a).