Question

state the null hypotheseis for:

e) A researcher hypothesizes that the average in cholesterol is lower associated with weight loss is really due to exercise. To test this, the researcher carefully controls for exercise while comparing the cholesterol levels of a group of subjects who lose weight by dieting with a control group that does not diet.

f) Suppose a study was conducted on the effectiveness of a class on "How to take tests." The SAT scores average of an experimental group and a control group were compared. (There were 100 subjects in each group.) The mean score of the experimental group was 503 and the mean score of the control group was 499.

g) The scores of a random sample of 8 students on a physics test are as follows: 60, 62, 67, 69, 70, 72, 75, and 78. Test to see if the sample mean is significantly greater than 65.

h)An experiment compared the ability of three groups of subjects to remember briefly-presented chess positions. determine which groups are significantly different from each other

Answer 1

Note: Data is nott provided for question (h), hence it is not answered.

Answers: e) The null hypotheses vs the alternative hypotheses is: H0:   vs Ha: where are the true population means for the cholesterol level of people who doesn't lose weight by dieting and those who diet to lose weight, respectively.

f) The null hypotheses vs the alternative hypotheses is: H0:   vs Ha: where are the true population means of the SAT scores of experimental and control groups respectively.

g) For the given problem we construct the null and alternative hypotheses as:

H0: mu = 65 vs Ha: mu > 65 [Since the claim was that, sample mean is actually more than 65]. mu = unknown true value of the parameter

The test statistic is T= (xbar-mu0)/(s/sqrt(n)) ; where xbar = sample mean, mu0 = the hypothesized value of the population mean, n = sample size, s = sample standard deviation, sqrt refers to the square root function. Under H0, T ~ t(n-1)

We reject H0 if T(observed) > t(alpha,(n-1)), where t(alpha,(n-1)) is the upper alpha point of the t - distribution with (n-1) degrees of freedom.   alpha = level of significance.

Here, T(observed) = 1.911181 and -t(alpha,(n-1)) = 1.894579 (Obtained from the probability table of Student's t distribution)

Hence, T(observed) > t(alpha,(n-1)).

Hence we reject H0 and conclude at a 5% level of significance on the basis of the given sample that there is enough evidence to support the claim that the average value of mean scores of the students on a Physics test is significantly greater than 65