Question

the sample measurements and use a t-test. 3. A manufact urer claims that the percentage of phosphorus ina at least 3 per cent. Ten small samples are taken from a batch d. The ten measure- and the percentage of phosphorus in each is measure ple mean of 2.5 per cent and a sample standard 5 per cent. Is this sample mean significantly below the alue? State the null hypothesis and the alternative hypothesis and say if l a one- or two-tailed test is required. on namnanv is approximately

Answer 1

Assume alpha = 0.05

One tail test

(1) Null and Alternative Hypothese The following null and alternative hypotheses need to be tested Ha: μ < 3 This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used (2) Rejection Region Based on the information provided, the significance level is α 0.05, and the critical value for a left- tailed test is tc--1.833. The rejection region for this left-tailed test is R-t: t< -1.833 (3) Test Statistics The t-statistic is computed as follows 2.5- 3 --3.162 s/Vn0.5/V10 (4) Decision about the null hypoth Since it is observed that t is rejected Using the P-value approach: The p-value is p concluded that the null hypothesis is rejected (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean u is less than 3, at the 0.05 significance level esIS 3.162 < tc 1.833, it is then concluded that the null hypothesis 0.0058, and sinc e p - 0.0058 < 0.05, it is