In testing the difference between two population means using two independent samples the population standard deviations were assumed to be known and the calculated test statistic equal 2.56 if the test was too detailed and a 5% level of significance had been specified what would be the most appropriate conclusion for the findings
Added by Miranda H.
Step 1
- Null hypothesis (H0): There is no difference between the two population means (μ1 = μ2). - Alternative hypothesis (H1): There is a difference between the two population means (μ1 ≠ μ2). Show more…
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In testing the difference between two population means using two independent samples, the population standard deviations are assumed to be known and the calculated test statistic equals 2.56. If the test is two-tail and 5% level of significance has been specified, the conclusion should be to: a. choose two other independent samples b. repeat using a one-tail test c. not to reject the null hypothesis d. reject the null hypothesis e. none of these
Marc L.
A two-tail test with a significance level of 0.01 led to a test statistic of 2.60. Which of the following are the correct conclusion and interpretation for the hypothesis test?
Hoan N.
A random sample of 49 measurements from a population with population standard deviation ́̑1 = 3 had a sample mean of x̄1 = 9. An independent random sample of 64 measurements from a second population with population standard deviation ́̑2 = 4 had a sample mean of x̄2 = 11. Test the claim that the population means are different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. The standard normal distribution. Samples are independent, the population standard deviations are known, and the sample sizes are sufficiently large. The student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The student's t. We assume that both population distributions are approximately normal with known standard deviations. (b) State the hypotheses. H0: ́̑1 ≠ ́̑2; H1: ́̑1 = ́̑2 H0: ́̑1 = ́̑2; H1: ́̑1 > ́̑2 H0: ́̑1 = ́̑2; H1: ́̑1 ≠ ́̑2 H0: ́̑1 = ́̑2; H1: ́̑1 < ́̑2 (c) Compute x̄1 - x̄2. x̄1 - x̄2 = -2 Compute the corresponding sample distribution value. (Test the difference ́̑1 - ́̑2. Round your answer to two decimal places.) 12.97 (d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.) 0.68 (e) Conclude the test. At the ́̑ = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ́̑ = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the ́̑ = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ́̑ = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. (g) Find a 99% confidence interval for ́̑1 - ́̑2. (Round your answers to two decimal places.) lower limit 0.25 upper limit 3.75
Adi S.
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