Question

A hypothesis test is to be performed with a Null hypothesis
**H _{o}: µ ≥ 15** and an alternative
hypothesis

1- What is type l error?

2- What is the chance of making a type I error in the above test?

3- What is a Type II error?

4- What value would the sample mean have to be less than to
reject H_{0}? (3dp)

5- if the real value µ=14 what is the probability that a type ll error occurs?

6- what will happen to the Type II error if the sample size decreases to 30 and all else remains unchanged. Including the answer to question 4 (Increase or Decrease)

Answer #1

It is desired to test the null hypothesis µ = 40 against the
alternative hypothesis µ < 40 on the basis of a random sample
from a population with standard deviation 4. If the probability of
a Type I error is to be 0.04 and the probability of Type II error
is to be 0.09 for µ = 38, find the required size of the
sample.

A hypothesis test will be performed to test the claim that a
population proportion is less than 0.70. A sample size of 400 and
significance level of 0.025 will be used. If = 0.62, find the
probability of making a type II error, β.

Assume that the population variance is unknown. We test the
hypothesis that Ho: µ=5 against the one-sided alternative H1: µ≠5
at a level of significance of 5% and with a sample size of n=30. We
calculate a test statistic = -1.699. The p-value of this hypothesis
test is approximately ？ %. Write your answer in percent form. In
other words, write 5% as 5.0.

. Consider the following hypothesis test: H0 : µ ≥ 20 H1 : µ
< 20 A sample of 40 observations has a sample mean of 19.4. The
population standard deviation is known to equal 2. (a) Test this
hypothesis using the critical value approach, with significance
level α = 0.01. (b) Suppose we repeat the test with a new
significance level α ∗ > 0.01. For each of the following
quantities, comment on whether it will change, and if...

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 =...

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...

In order to test HO: µ0 = 40 versus
H1: µ ≠ 40, a random sample of size n = 25 is
obtained from a normal population with a known σ = 6. My x-BAR mean
is 42.3 from my sample.
Using a TI 83/84 calculator, calculate my P-value with the
appropriate Hypothesis
Test.
Use a critical level α = 0.10 and decide to Accept or Reject
HO with the valid reason for the decision.
Group of answer choices
My...

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 test:
H0: µ = 15
Ha: µ ≠ 15
A sample of 50 provided a sample mean of 14.15. The population
standard deviation is 3.
Compute the value of the test statistic. (Round to two decimal
places).
What is the p-value? (Round to three decimal places)
At α=0.05, what is your conclusion? (Reject the null hypothesis)
or (Do not reject the null hypothesis)

Consider the following hypothesis test: H0: µ = 15 Ha: µ ≠ 15 A
sample of 50 provided a sample mean of 14.15. The population
standard deviation is 3. A.) Compute the value of the test
statistic. (Round to two decimal places). B.) What is the p-value?
(Round to three decimal places) C.) Using a=0.01, what is your
conclusion? D.) Using the critical value approach for the 99%
confidence level, what is the critical value? what is the rejection
rule?...

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