Question

0.674	0.841	1.036	1.282	1.645	1.960	2.054	2.326	2.576	2.807	3.091	3.291
confid.	50%	60%	70%	80%	90%	95%	96%	98%	99%	99.5%	99.8%	99.9%

Z<0 chart
Z>0 chart
T-chart
chi-square chart
Chi-square calculator
Please use the relevant chart(s) linked or displayed here to answer all questions.

From a simple random sample of 9 individuals, we record their normal walking speed and their walking speed while carrying the Ring of Power. The nine differences in speed (without - with) are recorded: their mean is 1.5 miles/hr and their standard deviation is 2 miles/hr. Do we have evidence at the following levels that on average, the Ring of Power slows one's walking speed?

The p-value for this hypothesis test is (on relevant chart linked above, as displayed there) is between ? (lower) and ? (higher).

Answer 1

we have to test that if difference=without -with have average value more than zero

so

we have sample mean of difference=m=1.5   

sample sd for difference =S=2

n=9

now test statistics is given by

df=n-1=9-1=8

test is right tailed so

P-value =P(t>2.25)=0.03

we have used T statistics (chart) as we do not have knowledge of population standard deviation

since P value is 0.03 which is more than 0.01 but less than 0.05 so we will reject H0 at 0.05 level of significance hence there is enough evidence at 0.05 level of significance to conclude Ring of Power slows one's walking speed.