Question

The number of hours worked per year per adult in a state is normally distributed with a standard deviation of 37. A sample of 115 adults is selected at random, and the number of hours worked per year per adult is given below. Use Excel to calculate the 98% confidence interval for the mean hours worked per year for adults in this state. Round your answers to two decimal places and use ascending order.

Number of hours
2250
1987
2029
2018
1938
2197
2099
2228
2245
1913
1903
2298
2231
2200
1902
2161
2211
2124
2082
2257
2087
2123
1929
1948
2124
2013
1973
2000
2030
1932
1993
2014
2118
1900
2195
2222
2035
2088
2010
1962
2166
1918
2070
2277
2114
1975
2045
2050
1921
2103
1954
2017
2235
1993
2156
1984
2057
2200
2133
2144
2145
2219
2222
2210
2143
2163
2168
2246
2186
1907
2072
2142
2187
2036
2207
2270
2262
2159
1914
1926
2261
2006
1948
2028
2256
2182
1955
1969
1941
1924
2176
2256
2051
2111
2221
2222
2190
2068
1942
2024
2258
2201
2085
2061
2004
2260
2136
2244
1989
1941
2297
2159
2260
2093
2293

Answer 1

Given,

confidence level = 98% = 0.98

Significance level = = 1 - 0.98 = 0.02

Standard deviation = = 37

Sample size = n = 115

Sample mean = = 2098.06087                  { Using Excel function ,   =AVERAGE( select all data ) }

Confidence interval for the population mean is given by,

Where , E is margin of error.

Using Excel function ,    = CONFIDENCE.NORM( ,standard_dev, size)

E = CONFIDENCE.NORM( 0.02 , 37 , 115 ) = 8.02652

So, 98% confidence interval for the population mean is ,

CI = ( 2090.03 , 2106.09 )

The 98% confidence interval for the mean hours worked per year for adults in this state is ( 2090.03, 2106.09)