Question 1206830
A survey of 45 randomly selected iPhone owners showed that the purchase price has a mean of $426 with a sample standard deviation of $190.

Compute the 95% confidence interval for the mean. (Round the final answers to 2 decimal places.)


the sample size is 45.
the sample mean is 426.
the sample standard deviation is 190.


the standard error is equal to standard deviation / sqrt(sample size) = 190 / sqrt(45) = 28.3235.


t-score is indicated because standard deviation is taken from the sample rather than from the population.


t-score formula is t = (x-m)/s


t is the t-score
x is the maximum and minimum sample mean at 95% two tail confidence interval.
m is the given sample mean.
s is the standard error.


from the provided t-score table you should be able to derive that the critical t-score with 44 degrees of freedom at 95% two tail confidence interval is plus or minus 2.015.


the table just shows 2.015.


you have to extrapolate from that to determine that you need 2.015 on the high end of the confidence interval and -2.015 on the low end of the confidence interval.


on the low end of the confidence interval, the t-score formula becomes:


-2.015 = (x - 426) / 28.3235.

solve for x to get x = -2.015 * 28.3235 + 426 = 368.93.


on the high end of the confidence interval, the t-score formula becomes:


2.015 = (x - 426) / 28.3235.


solve for x to get x = 2.015 * 28.3235 + 426 = 483.07


your two tail 95% confidence interval is 368.93 to 483.07.


that should be your answer.