Question

This Question: 1 pt 2 of 10 (0 completely Thi To test Hop-20 versus H 2 0, a simple random sample of size = 16 is obtained from a population that is known to be normally debuted. Answer parts card) IIClick here to view the t-Distribution Area in Right Tail (a) If x= 18.2 and ss 4.3, compute the best stastic - (Round to two decimal places as needed.) (b) Draw a I-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region? O A (c) Approximate the P-value. Choose the correct range for the P-value below. O A 0.15<P-value < 0.20 OB. 0.10 < P-value < 0.15 OC. 0.05<P-value <0.10 OD. 0.20<P-value < 0.25 (d) If the researcher decides to test this hypothesis at the 0.05 level of significance will the researcher reject the null hypothesis? OA. The researcher will reject the null hypothesis since the value is less than O B. The researcher will reject the null hypothesis since the P-value is not less than a O C. The researcher will not reject the null hypothesis since the value is less than a Click to select your answer(s). MacBook Pro

Answer 1

Given that,
population mean(u)=20
sample mean, x =18.2
standard deviation, s =4.3
number (n)=16
null, Ho: μ=20
alternate, H1: μ<20
level of significance, α = 0.05
from standard normal table,left tailed t α/2 =1.753
since our test is left-tailed
reject Ho, if to < -1.753
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =18.2-20/(4.3/sqrt(16))
to =-1.6744
| to | =1.6744
critical value
the value of |t α| with n-1 = 15 d.f is 1.753
we got |to| =1.6744 & | t α | =1.753
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1.6744 ) = 0.05738
hence value of p0.05 < 0.05738,here we do not reject Ho
ANSWERS
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a.
null, Ho: μ=20
alternate, H1: μ<20
test statistic: -1.6744
critical value: -1.753
decision: do not reject Ho
b.
option:B
left tail area is shown in the figure.
p-value: 0.05738
option :C
p value is between 0.05 to 0.10
d.
we do not have enough evidence to support the claim that mean is less than 20.
option:C