Question

Question 1.

A class survey of 400 students was given in which students at College ABC claimed to study an average of 15.8 hours per week. Consider these students as a simple random sample from the particular population of College ABC students. We want to investigate the question: Does the survey provide good evidence that students study more than 15 hours per week on average? Assume the population of hours studied is normal with a standard deviation of 4.

a) State the null and alternate hypothesis in terms of the mean study time in hours for the population.
b) Is this a one-tailed test or two-tailed test?
c) Determine the value of the test statistic.
d) Sketch a normal shape curve and identify the test statistic.
e) Indicate the p-value of the test. Use the standard normal table. Shade the area under the normal curve corresponding to the p-value.
f) State your conclusion to the statistical problem in terms of the null hypothesis, and your conclusion to the practical problem.

Answer 1

given

sample size =n=400

sample mean =m =15.8

population Standard deviation =SD=4

we need to test that if study hours per week is 15 or more than 15 hence

a)

b)

since in alternative hypothesis its showing average study hours per week is more than 15 that means its indicating only in one direction that right to value 15 hence

it's one-tailed test (right-tailed)

c)

value of test statistics is given by

d)

e)

P value =P(Z>4)=0.000032

f)

Since P-Value is very small so we can reject H0 on any possible level of significance so

we have enough evidence to conclude that average number of hours of study per week is more than 15.