help me please to solve this problem

Question

You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:

71.3
69.2
68
62.8
98.6
26.2
63.8
60.3

Find the 80% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place).

80% C.I. = Incorrect

Answer should be obtained without any preliminary rounding.

Answer 1

Hi Alina,

You were not given a population standard deviation, so you have to use a t-confidence interval. Formula for that is:

CI = xbar +/- t*SE, SE = s/sqrt(n)

xbar= sample mean

t* = t-critical value obtained from t-table or software

SE= standard error

s= sample standard deviation

n= sample size

To compute xbar, add up all values and divide by 8.

To compute s, use either a TI-80s series calculator or software. Standard deviation is difficult and error-prone to compute manually.

To get t*, you first need degrees of freedom. For a one-sample t test, this is:

Df= n-1; n= sample size = 8

df=7

Go to a t-table online. Look up 7 degrees of freedom at the left and 90% at the bottom. You should come up with t* = 1.415.

Finally, for standard error, divide your sample standard deviation by the square root of your sample size, 8.

SE = s/sqrt(8)

Once you have xbar, t*, and standard error, plug those values into the original formula and round both bounds to two decimals.

CI = xbar +/- t*SE

You should be good to go from here. I hope this helps.