In a medical experiment, scientist want to test if the new drug is more effective than the old one. They choose two group of patients randomly. There are 33 persons in the first group for new medicine, with the mean of 5.74, standard deviation of 6.74, and 25 people in the second group for the old one with the mean of 2.77, standard deviation of 6.28. At the 5% level of significance calculate the statistical value. 1 represent the new medicine group, and 2 represent the group that takes the old one. Assume that two populations are normally distributed and their variences are euqal. (Round your answer to two decimal places)

A sample of 39 observations is selected from a normal population. The sample mean is 43, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.02 significance level.

We wish to conduct a test of hypothesis on two independent population means. The alternative hypothesis of the test states that the means differ. Both populations are assumed normal with equal variance. We draw 10 observations for the first sample and 20 observations for the second sample. State the decision rule for the test if the level of significance is 0.01.Question 2Select one:a.we reject Ho if t > 2.4671b.we reject Ho if t <-2.4671 or t > 2.4671c.we reject Ho if t > 2.3263d.we reject Ho if t <-2.7633 or t > 2.7633

a) A random sample of eight observations was taken from a normal population. The sample mean and standard deviation are 75 and 50, respectively. Can we infer at the 10% significance level that the population mean is less than 100?b) Repeat part (a) assuming that you know that the population standard deviation is 50.c) Review parts (a) and (b). Explain why the test statistics differ.

group of 200 patients tested a new medication.Some tried the new medication, and the rest took the old medication.The results are reported in the following two-way frequency table.Improvement No improvementNew medication 27 63Old medication 37 73A patient is chosen at random from this group.Complete the following. Write your answers as decimals.(a)Find the probability that the patient showed improvement.=P(improvement)(b)Find the probability that the patient showed improvement, given that he took the new medication.=P(improvement | new medication)(c)Is there evidence that a patient who takes the new medication is more likely to show improvement than a randomly chosen patient from the group?Yes, because the probability found in part (b) is much

The professior of a university believes that the average age of the bachelor students  is 23. However, the tutor belives that the average age of the bachelor students differs from 23. To test the claim, they randomly selected 100 students, the average age was found to be 24.2 years. Assume the population standard deviation for the student age is 6 years. At the 1% level of significance, what is the test statistics?