In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to cons

Elleanor Mckenzie 2021-01-31 Answered
In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean:
For a two-tailed hypothesis test with level of significance a and null hypothesis H0:μ=k we reject Ho whenever k falls outside the c=1α confidence interval for μ based on the sample data. When A falls within the c=1α confidence interval. we do reject H0.
For a one-tailed hypothesis test with level of significance Ho : μ=k and null hypothesiswe reject Ho whenever A falls outsidethe c=12α confidence interval for p based on the sample data. When A falls within the c=12α confidence interval, we do not reject H0.
A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as p, μ1μ2, and p1,p2.
(a) Consider the hypotheses H0:μ1μ2=O and H1:μ1μ2 Suppose a 95% confidence interval for μ1μ2 contains only positive numbers. Should you reject the null hypothesis when α=0.05? Why or why not?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

d2saint0
Answered 2021-02-01 Author has 89 answers
The level of significance, α=0.05
The null hypothesis:
H0:μ1μ2=0
The alternative hypothesis:
H0:μ1μ20
Here, from above hypothesis D = 0 and we know that for a two-tailed hypothesis test with level of significance α, we reject H0 whenever D falls outside the c=1α confidence interval for μ based on the sample data. If a 95% confidence interval for μ1μ2 contains only positive numbers then we have to reject H0 at the level of significance α=0.05.
Since, the confidence interval does not contain D = 0 and hence it falls outside the 95% confidence interval.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2022-04-15
Least squares regression analysis is a common method for modelling trip generation. What are the main assumptions of the least squares regression analysis in that context? Discuss with examples the consequences of violating two of these assumptions.
asked 2022-05-21
The test statistic is z = 2.75, the critical value is z = 2.326. The probability value is_________.
Select one:
a. not measurable
b. greater than the significant level
c. equal to the significant level
d. less than the significant level
asked 2022-03-18
A study of the population of NUIG students showed that out of a sample of 155 students surveyed, 45 said they regularly cooked their own food during term time.Carry out a hypothesis test to determine if this gives evidence that more than 25% of the population of NUIG students regularly cooked their own food during term time, i.e test the hypotheses for true population proportion, H0: p= 0.25 versus Ha: p > 0.25, at significance level α = 0.05
Complete the test by filling in the blanks in the following:
An estimate of the population proportion is .The standard error is . (3 dec places)The distribution is (examples: normal / t12 / chisquare4 / F5,6).The test statistic has value TS=. (2 dec places)Testing at significance level α = 0.05, the rejection region is: greater than (2 dec places).There (is / is no) evidence to suggest that the true proportion of the population of all NUIG students who regularly cooked their own food during term time, p, is greater than 0.25.
asked 2020-11-26
State the conclusions about three tests at 5% level.
asked 2022-04-24
In conducting a significance test, is it easier or harder to reject the null hypothesis when the sample size is 1,500 compared to a sample size of 1,000?
a) easier
b) harder
asked 2020-12-24

In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean: For a two-tailed hypothesis test with level of significance a and null hypothesis H0:mu=k we reject Ho whenever k falls outside the c=1α confidence interval for mu based on the sample data. When A falls within the c=1α confidence interval. we do reject H0. For a one-tailed hypothesis test with level of significance Ho : mu = k and null hypothesiswe reject Ho whenever A falls outsidethe c=12α confidence interval for p based on the sample data. When A falls within the c=12α confidence interval, we do not reject H0. A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as p,μ1μ2, and p1,p2. (b) Consider the hypotheses H0:p1p2=O and H1:p1p2= Suppose a 98% confidence interval for p1p2 contains only positive numbers. Should you reject the null hypothesis when alpha = 0.05? Why or why not?

asked 2022-05-01
Show that the significant value of t at level of significance a for one-tailcd test is cqual to that of t at 2α significance level for two-tailed test.