Question

We adopt α=.05 and test the hypothesis Ho: μx=50. What conclusion should we draw if... (a) n=10, tcalc = +2.10, and Ha: μx ≠ 50? (b) n=20, tcalc = +2.10, and Ha: μx ≠ 50? (c) n=10, tcalc = +2.10, and Ha: μx > 50? Show the critical value of t for each part.

Answer #1

(A) given that sample size n = 10

degree of freedom = n-1

= 10-1

= 9

using excel function T.INV.2T(alpha,df)

setting alpha = 0.05 and df= 9

t critical = T.INV.2T(0.05,9) = -2.262 and +2.262

t statistic is between the t critical values. So, result is insignificant and we failed to reject the null hypothesis

(B) given that sample size n = 20

degree of freedom = n-1

= 20-1

= 19

using excel function T.INV.2T(alpha,df)

setting alpha = 0.05 and df= 19

t critical = T.INV.2T(0.05,19) = -2.093 and +2.093

t statistic is outside the t critical values. So, result is significant and we can reject the null hypothesis

(C) given that sample size n = 10

degree of freedom = n-1

= 10-1

= 9

using excel function T.INV(alpha,df)

setting alpha = 0.05 and df= 9

t critical = T.INV(0.05,9) = 1.833

t statistic is greater than t critical value. So, result is significant and we can reject the null hypothesis

In a test of the hypothesis Ho: μ = 50
versus Ha: μ ≠ 50,
with a sample of n = 100 has a Sample Mean = 49.4 and Sample
Standard Deviation, S = 4.1.
(a) Find the p-value for the test. (b)
Interpret the
p-value for the test, using
an α =
0.10.

The p-value and the value of α for a test of Ho: μ =
150 are provided for each part. Make the appropriate
conclusion regarding Ho.
P-value = .217, α = .10
P-value = .033, α = .05
P-value = .001, α = .05
P-value = .866, α = .01
P-value = .025, α = .01

The p-value and the value of α for a test of Ho: μ =
150 are provided for each part. Make the appropriate
conclusion regarding Ho.
P-value = .217, α = .10
P-value = .033, α = .05
P-value = .001, α = .05
P-value = .866, α = .01
P-value = .025, α = .01

Test Ho: µ =100; H1: µ < 100, using n = 36 and alpha = .05 If
the sample mean=106 and the sample standard
deviation = 15, which of the following is true?
A. test statistic = 2.4; the critical value = -1.69; we fail to
reject Ho.
B. test statistic = 1.96; the critical value = -1.69; we fail to
reject Ho.
C. test statistic = 2.40; the critical value = -1.69; we reject
Ho.
D. test statistic =...

Given that r= .8789 and n=4, test the hypothesis that
Ho: ρ = 0
Ha
:ρ ≠ 0
Assume α = .10, compute the T and state whether or not you will
reject or fail to reject the null hypothesis.

1. Consider the following hypothesis test: Ho : μ = 15 H1 : μ ≠
15 A sample of 50 provided a sample mean of 15.15. The population
standard deviation is 3. a. Compute the value of the test
statistic. b. What is the p value? c. At α = 0.05, what is the
rejection rule using the critical value? What is your
conclusion?
2. Consider the following hypothesis test: Ho: μ ≤ 51 H1: μ >
51 A sample...

3. Given that r= .9679 and n=4, test the hypothesis that Ho: ρ =
0 Ha :ρ ≠ 0
Assume α = .10, compute the T and state whether or not you will
reject or fail to reject the null hypothesis.

1. Consider the following hypothesis test: Ho: μ = 15 H1: μ ≠
15
A sample of 50 provided a sample mean of 15.15. The population
standard deviation is 3.
a. Compute the value of the test statistic. b. What is the p
value? c. At α = 0.05, what is the rejection rule using the
critical value? What is your conclusion?

consider the following hypothesis ho: u=470 ha: u does not equal
470
The population is normaly distributed with a population standard
deviation of 53
a-1 calculate the value of the test statistic with x= 492 and
n=90
a-2 what is the conclusion at 10% significance level
a-3 interpret the results at a=.1
b-1 calculate the value of the test statistic at x= 438 and
n=90
b-2 what is the conclusion at 5% significance level
b-3 interpret the results at a=...

Consider the following hypothesis test for the mean of a
normally distributed population: Ho:
μ=80. A random sample of size 40 is to be taken. The
population standard deviation is 20. Write the rejection rule using
critical value method; use α=4%. Please clearly identify
the test-statistic (t or z or F etc).

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