Question

Ruth read a report that the national weekly spending average for teens in the age group 12-15 years is $42. She took a random sample of 60 teens and found that they spent an average of $35 per week with a standard deviation of $ 7.50. Test the claim that teens from this area spend less than the national average. Use a 5% significance level.

Answer 1

Solution:

Given the hypothesis

H0: = 42 ....null hypothesis

H1: < 42 ....alternative hypothesis

n = 60 ....sample size

= 35    ...sample mean

s = 7.50 ....Sample standard deviation

= 5% = 0.05   .... level of significance

Since population SD is unknown,we use t test.

The test statistics t is given by ..

t =  

= (35 - 42)/(7.50/60)

t = -7.230

Now, < sign in H1 indicates that the left tailed test.

So, the critical value is   i.e.  

The critical region : t <    

  =   _0.05,59 = 1.671 (using t table)

= -1.671

t = -7.230 <   -1.671

So we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that this area spend less than the national average.