Consider the test of H0 : µ = 300 Vs. Ha : µ ≠ 300 using...
Consider the test of H0 : µ = 300 Vs. Ha : µ ≠ 300 using a
random sample of 36 values and α = 5%. Assume that σ = 40. Find the
power of the test when µa = 285.
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To test the hypothesis H0 : µ = 5 vs. Ha : µ 6= 5, a random
sample of 18 elements is selected which yielded a sample mean of x¯
= 4.6 and a sample standard deviation of s = 1.2. The value of the
test statistic is about:
(a) −2.121 (b) −1.923 (c) −1.414 (d) 0.345 (e) 1.455
5. Consider the hypothesis test H0 : µ = 18, Ha :µ ≠ 18. A
sample of size 20 provided a sample mean of 17 and a sample
standard deviation of 4.5.
a. 3pts.Compute the test statistic.
b.3pts. Find the p-value at the 5% level of significance, and
give the conclusion.
c. 5pts.Make a 99% confidence interval for the population
mean.
d. 5pts.Suppose you have 35 observations with mean17 and S.d.
4.5. Make a 90% confidence interval for the population...
We want to test H0 : µ ≥ 200 versus Ha : µ < 200 . We know
that n = 324, x = 199.700 and, σ = 6. 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...
2. Suppose we have the hypothesis test
H0 : µ = 200
Ha : µ > 200
in which the random variable X is N(µ, 10000). Let the critical
region C = {x : x ≥ c}.
Find the values of n and c so that the significance level of
this test is α = 0.03 and the power of µ = 220 is 0.96.
Suppose an experimenter wishes to test
H0: µ = 100 vs H1: µ ≠ 100
at the α = 0.05 level of significance and wants 1 – β to equal
0.60 when µ = 103. What is the smallest (i.e. cheapest) sample size
that will achieve the objective? Assume the variable being measured
is normally distributed with σ = 14.
You are testing H0: µ = 0 against Ha: µ > 0 based on
an SRS of 15 observations from a Normal population.
What values of the t statistic are statistically
significant at the a = 0.005 level?
t < - 3.326 or t > 3.326
t > 2.977
t < - 3.286 or t > 3.286
To study the metabolism of insects, researchers fed
cockroaches measured amounts of a sugar solution. After 2, 5, and
10 hours, they dissected...
QUESTION 1:
You are testing H0: µ = 0 against
Ha: µ > 0 based on an SRS of 16 observations
from a Normal population.
What values of the t statistic are statistically
significant at the a = 0.005 level?
t < - 3.286 or t > 3.286
t > 2.947
t < - 3.252 or t > 3.252
QUESTION 2:
A study of commuting times reports the travel times to work of a
random sample of 22 employed adults...
Determine the p-value for testing: H0: µ = 15
Ha: µ > 15
when a random sample of size 18 was
taken from a normal population whose standard deviation is unknown
and the value of the test statistic equals 2.35.
The 98% confidence interval for the population proportion of
successes when a random sample of size 80 was taken from a very
large population and the number of successes in that sample was
counted to be 20. No concluding statement is...
Consider the following hypothesis test: H0: ? = 16 Ha: ? ? 16 A
sample of 40 provided a sample mean of 14.17. The population
standard deviation is 6. a. Compute the value of the test statistic
(to 2 decimals). b. What is the p-value (to 4 decimals)? c. Using ?
= .05, can it be concluded that the population mean is not equal to
16? Answer the next three questions using the critical value
approach. d. Using ? =...
(a) Test H0 : p = 1/2 vs. Ha : p does not equal 1/2 for X ∼
Binomial(n=45,p), when we observe 16 successes.
(b) Calculate a 95% confidence interval for p for the data
above.
(c) Calculate a 95% confidence interval for p when X ∼
Binomial(15,p) and we observe only successes