Question

In: Statistics and Probability

A researcher did a one-tailed hypothesis test using an alpha level of .01, H0 was rejected.A...

A researcher did a one-tailed hypothesis test using an alpha level of .01, H0 was rejected.A colleague analyzed the same data but used a two-tailed test with α=.05, H0 was failed to reject. Can both analyses be correct? Explain your answer.

Solutions

Expert Solution

Yes Both analysis can be correct.

Prove it by an example :

Null hypothesis : Ho:

Alternate hypothesis : Ha(Two tailed test)

Given
Hypothesized Mean : 1
Sample Mean : 1.2
Population Standard Deviation : 0.4
Sample Size : n 12
Level of significance : 0.05

p-value for two tailed test :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0834 > 0.05:Level of significance); Fail to Reject Null Hypothesis

For the same data;

The hypothesis is changed to make it into one tailed test.

Null hypothesis : Ho:

Alternate hypothesis : Ha :

p-value for right tailed test :

As P-Value i.e. is less than Level of significance i.e (P-value:0.0417 < 0.05:Level of significance); Reject Null Hypothesis


Related Solutions

A researcher did a one-tailed hypothesis test using an alpha level of .01, H0 was rejected....
A researcher did a one-tailed hypothesis test using an alpha level of .01, H0 was rejected. A colleague analyzed the same data but used a two-tailed test with α=.05, H0 was failed to reject. Can both analyses be correct? Explain your answer. I searched for this but found another answer which did not accurately reflect the original one-tailed using .01.
For a two-tailed hypothesis test at the significance level alpha, the null hypothesis H0: μ =...
For a two-tailed hypothesis test at the significance level alpha, the null hypothesis H0: μ = μ0 will be rejected in favor of the alternative hypothesis Ha: μ≠ μ0 if and only if μ0 lies outside the (1 - α) level confidence interval for μ. Illustrate the preceding relationship by obtaining the appropriate one-mean z-interval for the data below. Suppose the mean height of women age 20 years or older in a certain country is 62.8 inches. One hundred randomly...
If a researcher conducted a 2-tailed, non-directional hypothesis test with an alpha level of .02, what...
If a researcher conducted a 2-tailed, non-directional hypothesis test with an alpha level of .02, what would be the corresponding critical value z-score(s)? a.-2..32 b.2.325 and -2.325 c.+1.96 and -1.96 d. 2.055 and -2.055
For a two tailed hypothesis test at the significance level a, the null hypothesis H0: M=M0...
For a two tailed hypothesis test at the significance level a, the null hypothesis H0: M=M0 will be rejected in favor of the alternative hypothesis Ha: M does not = M0 lies outside the (1-a) level confidence interval for M. Illustrate the preceding relationship by obtaining the appropriate one mean t interval for the data below. According to a survey, the average person watched 4.53 hours of television per day in 2005. A random sample of 20 people gave the...
FILL IN THE BLANKS: At an alpha level of .01, test the null hypothesis against the...
FILL IN THE BLANKS: At an alpha level of .01, test the null hypothesis against the alternative that the mean WEIGHT of this sample is no different from the average population weight (u = 152 (151.67 pounds). (5 points) Step 1: Ho: = 152 pounds Ha: (not equal to) 152 pounds Step 2: Alpha level = 0.01 Step 3: Sampling distribution is ____________________ Step 4: Decision Rule — I will reject the Ho if the |_____| value falls at or...
4. Why would a researcher test a one-tailed vs. a two-tailed hypothesis? 5. Why would it...
4. Why would a researcher test a one-tailed vs. a two-tailed hypothesis? 5. Why would it be impossible for a researcher to test the following hypothesis using a t-test? H1: Female homicide offenders are more likely to be sentenced to maximum security prison than male homicide offenders. 6. If the null hypothesis in a t-test for two samples is not rejected, what conclusion can be drawn about the two means of the categorical variable? 7. Two groups of subjects participated...
Consider using a one-tailed as well as a two-tailed test of a null hypothesis regard- ing...
Consider using a one-tailed as well as a two-tailed test of a null hypothesis regard- ing an estimated regression coefficient. For the same significance level, which test is more stringent? In other words, for which test does rejection of the null hypothesis automatically imply rejection in the other test as well, but not vice versa? Explain.
Assume that a hypothesis test will be conducted using significance level α = .01 and alternative...
Assume that a hypothesis test will be conducted using significance level α = .01 and alternative hypothesis Ha: μ : ≠ 19.3. Furthermore, we will use the following sample data: n = 12, x-bar = 18.8, and s = 2.1.
1. Why would a researcher need to use a two-tailed test vs. a one-tailed test? 2.A...
1. Why would a researcher need to use a two-tailed test vs. a one-tailed test? 2.A scholar tests the following hypothesis:  Females have a greater number of delinquent peers than males.  In her test, she calculates a t value is -2.349.  Why would it be unnecessary to compare this test statistic to a critical t value?
Briefly describe a one-tailed vs two-tailed t-test in the context of hypothesis testing?
Briefly describe a one-tailed vs two-tailed t-test in the context of hypothesis testing?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT