Question

After interviewing a sample of 100 residents of New Taipei City, you find that the mean AGE of the sample respondents is 35 years with a standard deviation of 5.0, and that AGE seems fairly normally distributed. However, you are told that the average age of New Taipei City is less than 37 years ten years ago. Based on your sample data, you need to test whether the true average age of all New Taipei City residents is still less than 37 years now. At α = 0.05, calculate the test statistic and determine the statistical decision.

Select one:

a. t_STAT = 4 and reject H1.

b. t_STAT = - 4 and reject H1.

c. t_STAT = - 4 and reject H₀.

d. t_STAT = 4 and reject H₀.

Answer 1

Solution :

Given that,

= 37

= 35

s = 5

n = 100

The null and alternative hypothesis is ,

H0 :   = 37

Ha : < 37

This is the left tailed test .

Test statistic = t

= ( - ) / / n

= (35 - 37) / 5 / 100

= -4

tSTAT  = -4

P-value = 0.00

= 0.05  

P-value <

Reject the null hypothesis (Ho).

Correct Option :- c. tSTAT = - 4 and reject H0.