Question

You wish to test whether the number of fouls called in regular season games is different than during the NCAA tournament. The mean number of fowls called during all regular season gams is u = 40.1 During 16 randomly selected playoff games n = 16 the mean number of fowls is 38.1 and the standard deviation of the sample = 5.8 You calculate a 95% Confidence Interval for the mean number of fouls called during playoff games The lower value of the confidence interval is:______

Answer 1

the lower value of the interval = 35.26

Explanation:

The mean number is u = 40.1

n = 16

the mean number called x is 38.1

the standard deviation = 5.8

given a 95% Confidence Interval

The lower value of the confidence interval is?

solution

There is a infinite population and the standard deviation of the population is known,

the below formula is used for determining an estimate of the confidence limits of the population mean, i.e.

x ± ( zₐσ)/ √n

For a 95% confidence level, the value of za is taken from the confidence interval table = 1.96.

the confidence limits of the population=

x ± ( zₐσ)/ √n

38.1 ± (1.96*5.8)/ √16

38.1 ± 11.368/4

38.1 ± 2.842

40.942 or 35.258

Thus, the 95% confidence limits are 40.942 or 35.258

this prediction is made with confidence that it will be correct nine five times out of 100.

finally, the lower value of the interval = 35.26