For each of the following, (a) state the null hypothesis and (b) state the alter
ID: 3222629 • Letter: F
Question
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.
1.Rosie is an aging cocker spaniel in Elkin, NC 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.
Explanation / Answer
a) Null hypothesis H0: µ=115
b) Alternative hypothesis Ha:µ<115
c) We will use one-sample t-test as sample size is small and given that population is normal
We chose level of significance =0.01
d) degree of freedom =n-1=6-1=5
Left tailed Critical t=-3.365
e) Mean xbar=105
standard deviation s=11.26
sample size n=6
t-statistic =(xbar-115)/(s/sqrt(n))
=(105-115)/(11.26/sqrt(6))
=-2.175
f) We fail to reject the null hypothesis as calculated t>-3.365(critical-t)
g) AS we fail to reject the null,so p>0.01
h) We conclude that the heart rate is not slowing down.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.