I need help with homework question 4

Question

A researcher must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures

23.8

24.6

40.5

36.1

22.6

31.9

13.8

assuming the population of temperatures are normally distributed find the 98% confidence interval. Round the answers to two decimal places. Enter your answer as an interval of the form (LB,UB)

The researcher is 98% confident that the population average temperature is within the temperature interval.

Answer 1

Hi Morgan,

First, we need the sample mean xbar and standard deviation s. Calculating standard deviation manually is cumbersome, so use statistical software or a graphing calculator (TI-80s series). From TI-83:

xbar= 27.61

s= 9.09

Now, recall that this is a sample, not population, standard deviation, so we have to use a t-confidence interval:

CI = xbar +/- t*SE

xbar=sample mean

t*=t-critical value

SE=standard error= s/sqrt(n)

For this problem:

xbar= 27.61

s= 9.09

n= 7

SE= 9.09/sqrt(7)

SE= 3.44

Now, we need the critical value t*, which means we first need degrees of freedom (df)

df= n-1

n= 7

df= 7-1 = 6

Now, navigate to a t-table and look up 98% in the column and 6 in the row:

t*= 3.143

Now we can compute our confidence interval:

CI = xbar +/- t*SE

xbar = 27.61

t* = 3.143

SE = 3.44

CI= 27.61 +/- (3.143*3.44)

CI= (16.81, 38.41)

I hope this helps.