Need help with these (c) A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis on the standard treatment is two years. In an early trial, she tries the new treatment on three subjects who have an average survival time after diagnosis of four years. Although the survival time has doubled, the results are not statistically significant even at the 0.10 significance level. The explanation is- A. the sample size is small.- B. the calculation was in error. The researchers forgot to include the sample size.- C. that although the survival time has doubled, in reality the actual increase is really two years.- D. the placebo effect is present, which limits statistical significance.The correct answer is A. the sample size is small. (a) The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation \( \sigma = 25 \). You suspect that incoming freshmen have a mean \( \mu \) which is different from 115 because they are often excited yet anxious about entering college. To test your suspicion, you test the hypotheses \( H_0 : \mu = 115 \), \( H_a : \mu \neq 115 \). You give the SSHA to 25 students who are incoming freshmen and find their mean score. Based on this, you reject \( H_0 \) at significance level \( \alpha = 0.01 \). Which of the following would be most helpful in assessing the practical significance of your results?- \( \circ \) A. Report the P-value of your test.- \( \circ \) B. Test the hypotheses again, this time using significance level \( \alpha = 0.001 \).- \( \bullet \) C. Construct a 99% confidence interval for \( \mu \) in order to see the magnitude of the difference between 115 and your sample results.- \( \circ \) D. Take another sample and retest just to make sure the results are not due to chance.(b) In testing hypotheses, if the consequences of rejecting the null hypothesis are very serious, we should- \( \circ \) A. insist that the level of significance be smaller than the P-value.- \( \circ \) B. insist that the P-value be smaller than the level of significance.- \( \circ \) C. use a very small level of significance.- \( \bullet \) D. use a very large level of significance.

Hypothesis test are used to compare the sample and population. Hypothesis test are of two types, they are parametric and non parametric test. Parametric test follows the distribution of any form. Non parametric test does not follow any distribution. a) Given : Study based on the habits and attitudes among the college students are studied. Let the scores follow normal distribution with mean 115 and standard deviation 25 Let the null and alternate hypothesis be : H0 : μ=115H1 : μ≠115 For this, most helpful practical significance of the result is p value. option A is correct Incorrect options : Option B - Another level of significance used is wrong Option C - Confidence interval does not provide much significance Option D - Take another sample is wrongb) Given : Consequence of rejecting the null hypothesis is serious. Since, the level of significance is smaller then the chance of rejecting the null hypothesis is also high when it is not rejected. Hence, we use larger significance. i.e. 0.05 Option D is correct Incorrect options : Option A - Level of significance smaller then p value is wrong Option B - P value smaller than level of significance is wrong Option C - Smaller level of significance cause chance of rejecting the null hypothesis is also high when it is not rejected. c) Given : New treatment has been studied on three subject for more times. It is still not statistically significant, since the sample taken by the researcher for the new treatment is very small. Option A is correct Incorrect options : Option B - Sample size is included Option C - Study time increases does not cause changes Option D - It does not limit the statistical significance

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(c) A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis on the standard treatment is two years. In an early trial, she tries the new treatment on three subjects who have an average survival time after diagnosis of four years. Although the survival time has doubled, the results are not statistically significant even at the 0.10 significance level. The explanation is