Question

in a study, 8 long-haired rats and 7 short haired rats were selected at random the heights of these rats were then measured. let μ1 and μ2 be the population mean height of both the long-haired and short-haired rats (respectively). Assume that the length measurements for both populations are normally distributed.

long-haired rats: n1=8, x̄1=185, s1=8

short-haired rats: n1=7, x̄2=198, s2=10

i) what is the evidence (very strong / strong / moderate / little or no) we have against the null hypothesis? Give a reason why you chose your answer.

ii) specify the distribution (including the degrees of freedom if relevent) to be used for computing the p-value, and then compute (or bracket) the p-value witin the accuracy of the tables.

iii) compute the observed value of the test statistic for testing H0: μ1 - μ2 = 0 and H1: μ1 - μ2 ≠ 0.

Answer 1

To test, Ho: Mo - H2=0 s = pooled variance = th: Her er 70, (ni ~)s, " + (n - Der 2 Now, 80.62 2 n+n2 Ž Test statistie- to - ju Ho Entha-2- to S + 12 2.798 .. p-value = pltia 10, 0151 ? - 2. 798) Ho We thus 0.0151 we reject Since P-valere MOTO the nell hypothesis. Cuidence have strong against