Question

7. In 2010 the mean household expenditure for energy was $1450. An economist wants to test if that amount went up in the year 2014. He used a sample of 45 households and found the mean expenditure for energy in that sample to be $1570, and the standard deviation in that sample to be $415. Is there sufficient evidence to support his claim that the expenditure for energy went up, if we use the a=0.05 level of significance? Fill in all the information below: H: = H, rejected? (Answer yes or no) H, accepted? (Answer yes or no) Final conclusion: Is there significant evidence to believe that the economist is correct in his claim that the expenditure for energy went up? (Answer YES or NO):

Answer 1

Here the claim is that mean household expenditure has went up.As the null hypothesis always has an equality sign the claim will be alternate hypothesis.So alternate hypothesis and null hypothesis are:

$H_1:\mu>1450$

$H_0:\mu=1450$

As population standard deviation is not known we will use t distribution.

Now we will find test statistic.

$t=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{1570-1450}{\frac{415}{\sqrt{45}}}=1.94$

d.f= n-1 =45-1=44

P-value for one tailed t test with test statistic 1.94 and d.f. 44 with Excel formula=TDIST(x,d.f.,tail)=TDIST(1.94,44,1)=0.029

As P-value(0.029) is less than alpha(0.05) we reject the null hypothesis.

So we have enough evidence to support the calim that household expenditure has went up in 2014.