Question

Given the following data that was sampled from a normal population distribution: 1257 1306 1250 1292 1268 1316 1275 1317 1275

Determine a 95% confidence interval for the population mean. (round to nearest integer)

lower limit

upper limit

Answer 1

Let x be the given data values.

n = 9

Sample mean :

x
1257	729
1306	484
1250	1156
1292	64
1268	256
1316	1024
1275	81
1317	1089
1275	81

Sample standard deviation :

s = 24.9098 (Round to 4 decimal)

Here population standard deviation is not known so we use t interval.

Confidence level = c = 0.95

degrees of freedom = n - 1 = 9 - 1 = 8

t critical value = tc = 2.306 (From statistical table of t values)

Lower limit :

LL = 1264.853

LL = 1265 (Round to nearest integer)

Upper limit :

UL = 1303.147

UL = 1303    (Round to nearest integer)

Lower limit = 1265

Upper limit = 1303

95% Confidence interval for population mean is (1265, 1303)