Question

A study on crew teams analyzed the weights of randomly selected rowers from the Oxford and Cambridge crew teams. From data collected over past years, 8 Oxford and 8 Cambridge rowers were randomly selected, and their weight their senior year on the team was recorded. A curious crew fan wants to know if Oxford rowers weigh more on average than Cambridge rowers.

a) What parameter should be used to address the researcher’s question? µd µ1 -µ2

b).State the hypotheses you would test (be sure to define your order of subtraction) to address the fan’squestion.

c) You can assume the 16 rowers selected are a representative sample of rowers from the schools and that the weights are independent. What other assumption needs to be valid to perform your hypothesis test,

d) We will assume the conditions hold. Complete your test procedure, using the R output appropriate for your choice in a. to provide the numeric values of the test statistic and p-value for your hypotheses.

Paired t-test (CambridgeOxford) t = 0.7501, df = 7, p-value=0.2388 alternative hypothesis: true difference in means is greater than 0

Welch Two Sample t-test (CambridgeOxford) t = 0.4259, df = 13.775, p-value = 0.3384 alternative hypothesis: true difference in means is greater than 0

Test statistic:

(state the formula , how to calculate and then use the result above)

p-value : (write how to calculate and use the results above)

Interpretation of the p-value:

Circle your decision at a .10 significance level.

Reject Ho Do not reject Ho

State your conclusion (in the context of the problem) :

What type of error might you have made?

Type I Type II No Error

(Dataset not required to answer these questions)

Answer 1

a) difference between the two mean should be addressed.

b)

c) The sample should be coming from a random sample and normally distributed population.

d) This is a paired sample t test

test statistic : t = 0.7501,

df = 7,

p-value=0.2388

alternative hypothesis: true difference in means is greater than 0

since P value is greater than the significance level 0.10. We fail to reject the null hypothesis.

a type I error is the rejection of a true null hypothesis, while a type II error is the non-rejection of a false null hypothesis.

Since the null hypothesis is not rejected, there is a chance of Type II error