Question

1. For each of the 2 majors, conduct a full hypothesis test at the 10% significance level:
   • The mean ‘Cost’ for a college is $160,000.
2. 2. For Business versus Engineering majors conduct a full, two-sample, full hypothesis test at the 5% significance level (assume the variances are not equal):The average ’30-Year ROI’ for Business majors is less than for Engineering Majors.

1. 3.  In a highlighted box, explain how each hypothesis test contributes to the central question of which major would give the better ROI. Why do we need hypothesis testing? Isn't it enough to look at the sample of 20 schools and look at those numbers? What exactly does hypothesis testing do that looking at the numbers in the sample and saying "one is higher than the other" cannot do? This answer is critical to your final project. It demonstrates that you understand why you just can't look at the mean, median, and mode of the spreadsheet and "call it a day."  
2. engineering info is listed below:

3. School Type	Cost	30 Year ROI	Annual ROI
   Private	$221,700.00	$2,412,000.00	8.70%
   Private	$213,000.00	$2,064,000.00	8.30%
   Private	$230,100.00	$1,949,000.00	7.90%
   Private	$222,600.00	$1,947,000.00	8.00%
   Private	$225,800.00	$1,938,000.00	8.00%
   Public	$87,660.00	$1,937,000.00	11.20%
   Private	$224,900.00	$1,915,000.00	7.90%
   Private	$221,600.00	$1,878,000.00	7.90%
   Public	$125,100.00	$1,854,000.00	9.80%
   Private	$215,700.00	$1,794,000.00	7.90%
   Public	$92,530.00	$1,761,000.00	10.60%
   Private	$217,800.00	$1,752,000.00	7.70%
   Public	$89,700.00	$1,727,000.00	10.70%
   Private	$229,600.00	$1,716,000.00	7.50%
   Public	$101,500.00	$1,703,000.00	10.20%
   Public	$115,500.00	$1,694,000.00	9.70%
   Public	$104,500.00	$1,690,000.00	10.10%
   Public	$69,980.00	$1,685,000.00	11.50%
   Private	$219,400.00	$1,676,000.00	7.60%
   Public	$64,930.00	$1,668,000.00	11.70%

Answer 1

here we want to test the null hypothesis H0:$\mu$=160,000 and alternate hypothesis Ha:$\mu \ne$160,000

we use one sample t-test and

statistic t=($\bar{x}$-$\mu$)/(s/sqrt(n))=(217,350-160,000)/(66,385.12/sqrt(20))=3.863 with n-1=20-1=19 df

the typical critical t(0.1,19)=1.729 is less than calculated/observed t=3.863 , so we fail to accept H0 and conclude that ,the mean ‘Cost’ for a college is different than $160,000.

n=	20
mean=	$217,350.00
sample standard deviation= sd=	$66,385.12