a) Hypothesis-Testing Statement: The night life is more appealing to those aged 22 years and below.?

Question

sample size of 50 were taken. mean age is found to be 22.12, standard deviation as 14.883
Is the null hypothesis found to be true?

Answer 1

I would say yes since with this number of experimnts , the distribution obeys to a normal law and 95% of results is between mean+-2*standard deviation else

22+-2*14.883

Answer 2

I would say no, at least with this method of data analysis.
All you really have here is that of 50 people surveyed, they were all between the ages of 7 and 37, according to your mean and st. deviation.
You might try putting together a frequency table, if more than 25 of your survey participants are under 22, you can say it's supported. (but this kind of data is notoriously unreliable, demographic composition changes based on where and when you do your survey, so if you were running an actual experiment you would need a much bigger sample)

Answer 3

Ho: µ = 22
Ha: µ < 22
Assume α = 0.05
Z = -1.645 (one-tailed)
Z(calculated) = (x-µ)/(s/√n) = (22.12-22.00)/(14.883/7.071) = 0.057
The calculated Z is not in the critical area( 0.057> -1.645), so we cannot reject the null hypothesis and conclude it is true (cannot prove more appealing to those ≤ 22).