A random sample of n = 5 men between 30 and 39 years old is asked to do as many

Question

A random sample of n = 5 men between 30 and 39 years old is asked to do as many situps as they can in one minute. Table 1 reports the descriptive statistics for this study:

The investigators would like to construct a 98% confidence interval for the true average number of situps men in this age group can complete in 1 minute.

Note: you should carry at least 5 decimal precision for any intermediate calculations. Then round your answers as indicated.

A) The margin of error is:
     Round your answer to the nearest hundredth

B) The corresponding 98% confidence interval for the true population mean is: to sit-ups
When setting confidence intervals for discrete data investigators will round the lower endpoint down to the next lowest integer and the upper endpoint up to the next highest integer. You should express your answers using this convention

Explanation / Answer

a.
Margin of Error = t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
Mean(x)=27.8
Standard deviation( sd )=8.2
Sample Size(n)=5
Margin of Error = t a/2 * 8.2/ Sqrt ( 5)
= 3.747 * (3.66715)
= 13.74082
b.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=27.8
Standard deviation( sd )=8.2
Sample Size(n)=5
Confidence Interval = [ 27.8 ± t a/2 ( 8.2/ Sqrt ( 5) ) ]
= [ 27.8 - 3.747 * (3.66715) , 27.8 + 3.747 * (3.66715) ]
= [ 14.05918,41.54082 ]

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