Question

Instructor-created question Question Help The local veterinarian claims pugs weigh about 20 lbs on average. You think it may be less To test your hypothesis, you develop hypotheses, Hop=20 versus Hy <20, and record the weights of a simple random sample of 17 pugs. Assume the population of pug weights is known to be normally distributed Answer parts (a)(c) Click here to view the 1-Distribution Area in Right Tail. (a) If your mean sample weight is 18.4 pounds with a standard deviation of 3.6 pounds, compute the test statistic = (Round to two decimal places as needed) (b) Approximate the P-value. Choose the correct range for the P value below OAP value < 0.005 OB. 0.005 <P value < 0.01 OC 0.01 <P value < 0.05 OD. P value > 0.05 (c) of the researcher decides to test this hypothesis at the 605 level of significance will the researcher reject the null hypothesis? OA. The researcher will reject the null hypothesis since the P-value is not less than a OB. The researcher will not reject the nul hypothesis since the value is less than a OC. The researcher will not reject the nut hypothesis since the value is not less than a OD. The researcher will reject the null hypothesis since the P-value is less than a If the researcher decides to relect the nul hoothesis what is the probability of a TypeError? | Click to select your answers and then click Check Answer All parts showing Clear hack AWE

Answer 1

Ans : Let X be pugs weight

For given sample information is summarized below :

sample mean = 18.4 pounds

X

standard deviation s = 3.6 pound

sample size n = 17

here claim that pugs weight about 20 lbs on average

To Test of Hypothesis :

H₀ : $\mu$ = 20 versus H₁ : $\mu$ < 20

here we have to use left tailed t test for population mean

a)

Test Statistic :

(X t μο) (s/νη)

t= (18.4 – 20) (3.6/17)

t = -1.83

the tes stastics ;

t = - 1.83

b)

p value :

p- value = P(t <-1.83) = 0.0428

Approximetly the p - value

correct option is C

Ans : C. 0.01< p value < 0.05

here $\alpha$ = 0.05

Since p - value=0.0428 < $\alpha$ = 0.05 Then we reject H0 at 0.05 level of significance

c)

Ans : D. The researcher will reject the null hypothesis since the p - value is less than $\alpha$

P(type I error ) = P(Rject H0 / H0 is true)

= 0.04