Question

10. Use the table to answer the following questions: Variable Mean Std. Dev.N Hourly Wage 24.01 17.51 124,475 Age 42.22 10.31 124,475 (a) (10 Points) Construct a 95% confidence interval for the mean of the hourly wage. (b) (5 Points) is the mean hourly wage statistically different from zero at a 95% level of confidence? (c) (10 Points) Construct a 95% confidence interval for the mean of age. (d) (5 Points) is the mean age statistically differenct from zero at a 95% level of confindence? 11. Assume that the mean wage for men is 26.35 with a standard deviation of 19.07 and 63,203 observations. The mean wage for women is 21.58 with a standard deviation of 15.34 and 61,272 observations. (a) (2.5 Points) Construct a 95% confidence interval for the mean male wage. (b) (2.5 Points) Construct a 95% confidence interval for the mean female wage. (c) (10 Points) Are average wages for men and women statistically different from each other at a 0.05?

Answer 1

10)

a) Mean = 24.01

Sd = 17.51

95% CI for mean of hourly wage is given by,

$\bar{x}\pm z*\frac{s}{\sqrt{n}}$

$\bar{24.01}\pm 1.96*\frac{17.51}{\sqrt{124475}}$

$(24.11,23.91)$

There is statistical difference from zero. Because it doest not mean value.

c) 95% CI for mean of age is given by,

$\bar{x}\pm z*\frac{s}{\sqrt{n}}$

$42.22\pm 1.96*\frac{10.31}{\sqrt{124475}}$

$(42.28,42.16)$

There is statistical difference from zero. Because it doest not mean value.