Consider the following. (a) For the same data and null hypothesis, is the p-valu
ID: 3363110 • Letter: C
Question
Consider the following. (a) For the same data and null hypothesis, is the p-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain your answer. O The P-value for a one-tailed test is larger because the two-tailed test includes the area in only one tail. O The p-value for a one-tailed test is smaller because the two-tailed test includes the area in only one tail. O The P-value for a one-tailed test is larger because the two-tailed test includes the area in both tails. O The P.value for a one-tailed test is smaller because the two-tailed test includes the area in both tails. (b) For the same data, null hypothesis, and level of significance, is it possible that a one-tailed test results in the conclusion to reject Ho while a two-tailed test results in the conclusion to fail to reject Ho? Explain your answer. O No. The P-value for a one-tailed test might be smaller than a, while the p-value for a two-tailed test could be larger than a. o Yes. When the p-value for a one-tailed test is smaller than a, the P-value for a two-tailed test will also be smaller than a. o Yes. The p-value for a one-tailed test might be smaller than a, while the p-value for a two-tailed test could be larger than a. O No. When the p-value for a one-tailed test is smaller than cx, the -value for a two-tailed test will also be smaller than ca. (c) For the same data, null hypothesis, and level of significance, if the conclusion is to reject H, based on a two-tailed test, do you also reject H, based on a one-tailed test? Explain your answer. o Yes. If the two-tailed P-value is smaller than a, the one-tailed area is also smaller than a. O NO. If the two-tailed P.value is smaller than a, the one-tailed area will be larger than a. O No. If the two-tailed P-value is smaller than a, the one-tailed area is also smaller than a. o Yes. If the two-tailed P.value is smaller than a, the one-tailed area will be larger than a. (d) If a report states that certain data were used to reject a given hypothesis, would it be a good idea to know what type of test (one-tailed or two-tailed) was used? Explain your answer. O No. The conclusions can be different. o Yes. The conclusions will be the same. O No. The conclusions will be the same. o Yes. The conclusions can be different.Explanation / Answer
sOLUTIONA:
p for one taild=1/2 (p value of two tail)
For z=2.36
alpha=0.05
p value(one tail)=0.0091
p value(two tail)=0.018
THE PVALUE FOR ONE TAILED TEST IS SMALLER BECAUSE THE TWO TIALED TEST INCLDES THE AREA IN BOTH TAILS
optiond
Solutionb:
took sample data and calculated p value one tail
Owned <- c(0.003, 0.002 ,0.023, 0.102, 0.214, 0.225, 0.194 ,0.149, 0.053 ,0.035)
Rented <- c (0.008, 0.027 ,0.287, 0.376, 0.155 ,0.097, 0.031, 0.013 ,0.003, 0.003)
t.test(Owned,Rented,alternative="greater",mu=0.038)
output:
p-value = 0.7682
For two tal:
t.test(Owned,Rented,mu=0.38)
p-value = 1.392e-06
p=0.0000001392
set alpha=0.05
P value for one tail Fail to reject null hypothesis as p>alpha
P value for two tail Reject null hypothesis as p<alpha
dECSION RULE:
P<ALPHA REJECT HO
P>ALPHA FAIL TO REJECT HO
OPTIONC
Solutionc:
in gthe abova case
p>alpha(one tail)--LARGE VALUE
p<alpha (two tail)---SMALL VALUE
OPTIONB
Solutiond:
OPTIOND:
CONCLUSIONS ARE DIFFERENT