Question

To evaluate the effect of a treatment, a sample of n = 6 is obtained from a population with a mean of μ 80, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M- 72. Select a Distribution Distributions 02 If the sample variance is s2 54, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α-.05? Complete the following entries, using the Distributions tool as necessary. Test Statistic SM Type Value Critical Values Significant? If the sample variance is s2 150, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α-.05? Complete the following entries, using the Distributions tool as necessary. Test Statistic SM Type Value Critical Values Significant?

Answer 1

a) To test the hypothesis is that the treatment has a significant effect at 5% significance level. The null and alternative hypothesis is, H_0: mu = 80 H_0: mu notequalto 80 The t-test statistics is, t = x bar - mu_0/s/squareroot n = 72 - 80/squareroot 54/squareroot 6 = -2.67 The t-test statistics is -2.67. The t-critical values is, The sample size is small and two-tailed test. Look in the column headed alpha = 0.05 and the row headed in the t distribution table by using degree of freedom is, d.f. = n - 1 = 6 - 1 = 5 The t-critical value is plusminus 2.571 Decision The statistical decision is that the t-test statistics which is -2.67 is higher than t-critical value which is -2.571, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the treatment has a significant effect. The result is statistically significant. b) The t-test statistics is, \r\n