Question

The following data represent the number of housing starts predicted for the 2nd quarter (April through June) of 2014 for a random sample of 40 economists.

984 1260 1009 992 975 993 1025 1164 1060
992 1100 942 1050 1047 1000 938 1035 1030
964 970 1061 1067 1100 1095 976 1012 1038
929 920 996 990 1095 1178 1017 980 1125
964 888 946 1004

Required:
a. Draw a histogram of the data.
b. Construct a 95 % confidence interval for the population mean forecast of the number of housing starts in the second quarter of 2014.
c. Construct a 90% confidence interval for the population mean forecast of the number of housing starts in the second quarter of 2014

Answer 1

Kindly check attached picture ;

(999.494 ; 1046.056) ;

(1003.235 ; 1042.315)

Explanation:

Given the data:

888, 920, 929, 938, 942, 946, 964, 964, 970, 975, 976, 980, 984, 990, 992, 992, 993, 996, 1000, 1004, 1009, 1012, 1017, 1025, 1030, 1035, 1038, 1047, 1050, 1060, 1061, 1067, 1095, 1095, 1100, 1100, 1125, 1164, 1178, 1260

Using calculator to obtain the mean and standard deviation :

Mean, x = 1022.775

Standard deviation, s = 75.124

Sample size, n = 40

Zcritical at 95% = 1.96

Zcritical at 90% = 1.645

Using the relation :

x ± E

E = error margin = Zcritical * s / sqrt(n)

At 95% ;

Error margin = 1.96 * 75.124/ sqrt(40) = 23.281

At 90% ;

Error margin = 1.645 * 75.124/ sqrt(40) = 19.540

Confidence interval at 95%:

(1022.775 - 23.281) ;(1022.775 + 23.281)

(999.494 ; 1046.056)

Confidence interval at 90%:

(1022.775 - 19.540) ;(1022.775 + 19.540)

(1003.235 ; 1042.315)