Question

Word Problems with a Sample Data Set:

1. A sample of Full-time SUNY Poly students were asked how many credit hours they were taking this semester and the following information was obtained. Assume credit hours are approximately normally distributed.

16        18        12        17        20        18        15        14

*Round all final answers to 2 decimal places if necessary

1. Construct a 90% confidence interval for the population mean

2. Construct a 95% confidence interval for the population standard deviation

3. SUNY Poly claims that all their students average less than 18 credit hours per semester. Test SUNY’s claim at α = 0.05, what can you conclude about the claim?

Answer 1

a)

sample mean         x=	16.250
sample size             n=	8
sample std deviation s=	2.550
std error sx=s/√n=	0.9014

for 90% CI; and 7 df, critical t=		1.8950
margin of error E=t*std error                            =		1.7081
lower bound=sample mean-E =		14.5419
Upper bound=sample mean+E=		17.9581
from above 90% confidence interval for population mean =(14.54,17.96)

c)

	here n =	8
	s2=	6.500
Critical value of chi square distribution for n-1=7 df and 95 % CI
Lower critical value χ2L=		1.690
Upper critical valueχ2U=		16.013

for Confidence interval of standard deviation:
Lower bound =√((n-1)s2/χ2U)=(8-1)*6.5/16.013=		1.686
Upper bound =√((n-1)s2/χ2L)=(8-1)*6.5/2.841 =		5.189
from above 95% confidence interval for population standard deviation =(1.686<σ<5.189)

c)

null hypothesis: Ho:             μ		=	18
Alternate Hypothesis: Ha:μ		<	18
0.05 level with left tailed test and n-1= 7 df, critical t=			-1.895
Decision rule :                   reject Ho if test statistic t<-1.895
	population mean μ=	18
	sample mean         x=	16.250
	sample size             n=	8
	sample std deviation s=	2.550
	std error sx=s/√n=	0.9014
	test stat t='(x-μ)*√n/s=	-1.941

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that  their students average less than 18 credit hours per semester