The data shows the age distribution of the male and female respondents in the research. The total number of males is 704 while there are 791 female respondents. We can use the data on the sexes and age distribution to formulate and test the hypothesis by calculating the various parameters of statistical data as follows:
Statistical assumptions of this test include:( Ning-zhong S. & Jian T, 2008)
- The data is symmetrical about its mean
- The data assumes a normal probability distribution
- The distribution is completely defined by mean and standard distribution
- The data assumes a 95% level of confidence
In this case, the independent variable is the sex of the respondents while the age is the dependent variable in the distribution.
Null hypothesis- The average age of the respondents does not go beyond 50 years
Alternative hypothesis- The average age of female respondents exceeds that of the male.
In order to obtain a 95% confidence interval, we take the error to be 5%
Standard error = 5% = 0.05
Error/2 =0.05/2 = 0.025
Assuming a normal distribution, the Z value = 0.5-0.025
Z value = 0.475
95% confidence interval = Point estimate of mean +/- (Z X standard deviation/√sample size)
95% CI for males = 45.87 +/- (1.96 X 16.204/√704)
= 45.87 +/- 1.20
Either mean = 44.67 years
or = 47.07 years
We are 95% confident that the mean age of male respondents will fall between 44.67 and 47.07 years (Ning-zhong S. & Jian T, 2008)
.
For females: 95% CI = 46.54 +/- (1.96 X 17.095/√791)
= 46.54+/- 1.19
Either mean = 45.35 years
or = 47.73 years
We are 95% confident that the mean age of female respondents will fall between 45.35 and 47.73 years.
The null hypothesis will thus be accepted since it accurately as it states that the mean age of the respondents does not exceed 50 years.
Reference List
Ning-zhong S. & Jian T (2008): Statistical Hypothesis Testing: Theory and Methods. NY: HarperCollins
