For each of the following a state the null hypothesis and b

For each of the following, (a) state the null hypothesis and (b) state the alternate hypothesis, (c) state the type of test that you will use to test the hypothesis and the level of significance, (d) state the critical value , (e) calculate the z-statistic or the t-statistic, (f) state whether we shall reject or fail to reject the null hypothesis, (g) state the relation between the p-value and with an appropriate inequality, and (h) conclude the hypothesis test with an appropriate summarizing statement addressing the alternate hypothesis.

Rosie is an aging cocker spaniel in San Francisco, CA who gets regular check-ups from her owner, the local veterinarian. Let x be a random variable that represents Rosie’s resting heart rate (in beats per minute). The vet checked the Merck Veterinary Manual and found for dogs of this breed, = 115 beats per minute. Over the past six weeks, Rosie’s heart rate in beats per minute measured 93, 109, 110, 89, 112, and 117. The vet is concerned that Rosie’s heart rate may be slowing. At the = 0.01 level of significance, do the data indicate that this is the case? A normal probability plot shows the data to have a linear correlation of 0.938. A box-and-whiskers plot of the data shows no outliers.

Solution

a. Ho: u >= 115

b. Ha: u < 115

c. t test

d. This is a one-tailed test, with df = 6 - 1 = 5. Thus,

tcrit = -3.3649

e. t = (Xbar - 115) / (s/sqrt(6))

As Xbar = 105, s = 11.26, then

t = -2.1754 [answer]

f. FAIL TO REJECT THE NULL HYPOTHESIS, as t > tcrit.

g. p > alpha

h. There is no significant evidence that suggests that Rosie\'s heart rate is slower than the other dogs of her breed.