Question

*H*:_{0}*µ ≥*205 versus*H*:_{1}*µ <*205,*x*= 198,*σ*= 15,*n*= 20,*α*= 0.05

test
statistic___________ *p*-value___________ Decision
(circle one) Reject
the
*H _{0}* Fail
to reject the

*H*:_{0}*µ =*26 versus*H*:_{1}*µ<>*26,*x*= 22,*s*= 10,*n*= 30,*α*= 0.01

test
statistic___________ *p*-value___________ Decision
(circle one) Reject
the
*H _{0}* Fail
to reject the

*H*:_{0}*µ ≥*155 versus*H*:_{1}*µ <*155,*x*= 145,*σ*= 19,*n*= 25,*α*= 0.01

test
statistic___________ *p*-value___________ Decision
(circle one) Reject
the
*H _{0}* Fail
to reject the

Answer #1

#1.

Test statistic,

z = (xbar - mu)/(sigma/sqrt(n))

z = (198 - 205)/(15/sqrt(20))

z = -2.09

P-value Approach

P-value = 0.0183

As P-value < 0.05, reject the null hypothesis.

#2.

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (22 - 26)/(10/sqrt(30))

t = -2.191

P-value Approach

P-value = 0.0366

As P-value >= 0.01, fail to reject null hypothesis.

#3.

Test statistic,

z = (xbar - mu)/(sigma/sqrt(n))

z = (145 - 155)/(19/sqrt(25))

z = -2.63

P-value Approach

P-value = 0.0043

As P-value < 0.01, reject the null hypothesis.

H0: µ ≥ 20 versus H1: µ < 20, α = 0.05, sample mean = 19, σ =
5, n = 25

Suppose that we wish to test H0: µ = 20 versus
H1: µ ≠ 20, where σ is known to equal 7. Also, suppose
that a sample of n = 49 measurements randomly selected
from the population has a mean of 18.
Calculate the value of the test statistic Z.
By comparing Z with a critical value, test
H0 versus H1 at α = 0.05.
Calculate the p-value for testing H0 versus
H1.
Use the p-value to test H0 versus...

n=49, ? ̅ =8.5, µ=9.2, σ=2.6, α=.01, H0: μ
= 9.2, H1: μ ≠ 9.2.
Determine z-score __________
Determine p= ____________
Reject or fail to reject H0 __________

To test H0: σ=70 versus H1: σ<70, a random sample of size n
equals 25 is obtained from a population that is known to be
normally distributed.
(a) If the sample standard deviation is determined to be s
equals = 46.5, compute the test statistic.
(b) If the researcher decides to test this hypothesis at α=0.05
level of significance, use technology to determine the
P-value.
(c) Will the researcher reject the null hypothesis?
What is the P-Value?

Find the P-value.
H0: p=0.1 versus H1: p>0.1 n=250; x=30, α=0.01

To test H0: σ=2.2 versus H1: σ>2.2, a random sample of size
n=15 is obtained from a population that is known to be normally
distributed. Complete parts (a) through (d).
(a) If the sample standard deviation is determined to be s=2.3,
compute the test statistic.
χ^2_0=____
(Round to three decimal places as needed.)
(b) If the researcher decides to test this hypothesis at the
α=0.01 level of significance, determine the critical value.
χ^2_0.01=____
(Round to three decimal places as needed.)...

Consider the following hypothesis test:
H0:u equal to 25
H1: u> 25
α=0.05, σ= 2.4,n=30
what would be the cutoff value for y mean for the rejection of
h0?
If the true value is u=25.75, then what is the power of the
test?

1. In order to test H0: µ=40 versus H1: µ > 40, a random
sample of size n=25 is obtained from a population that is known to
be normally distributed with sigma=6.
. The researcher decides to test this hypothesis at the α =0.1
level of significance, determine the critical value.
b. The sample mean is determined to be x-bar=42.3, compute the
test statistic z=???
c. Draw a normal curve that depicts the critical region and
declare if the null...

We want to test H0 : µ ≤ 120 versus Ha : µ > 120 . We know
that n = 324, x = 121.100 and, σ = 9. We want to test H0 at the .05
level of significance. For this problem, round your answers to 3
digits after the decimal point.
1. What is the value of the test statistic?
2. What is the critical value for this test?
3. Using the critical value, do we reject or...

n=90, Y =18.8, S =15.3, α =0.05⇒tn−1,α/2 = t89,.025 =1.987
H0 : µ =21.7 versus HA : µ6=21.7
Rejection Region:|t|> t89,.025 =1.987
t =Y−µ0 S/sqrt(n) =18.8−21.7 15.3/p90 = −2.9 1.6128
=−1.798⇒|t|=1.798 < t89,.025 =1.987
Cannot reject H0 at 5% level. There is not sufﬁcient evidence to
support the average number of Type 2 ﬁbers is different from
21.7.
what is the p-value?

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