i need help Homework assignment A watch maker needs to estim

Homework assignment A watch maker needs to estimate the population mean failure time. A number of watches have been tested to failure. The data of time to failure in hours are 1250, 1320, 1542, 1464, 1275, 1260, 1420, 1442, 1454, 1375, 1255, 1322, 1552, 1664, 1285, 1257, 1329, 1548, 1474, 1575, 1250, 1320, 1542, 1464, 1275, 1260, 1420, 1442, 1454, 1375, 125, 1322, 1552, 1664, 1285, 1257, 1329, 1548, 1474, 1575 and 1353. Estimate the population mean failure time with a confidence level of 90%.

Solution

Given a=0.1, Z(0.05) = 1.645 (from standard normal table)

So 90% confidence interval is

xbar +/- Z*s/vn

--> 1401.93 +/- 1.645*123.32/sqrt(41)

--> (1370.248, 1433.612)

count	41
mean	1,401.93
population variance	15,207.19
population standard deviation	123.32