Need help with this and i require all workings

a) The University of the East Europe is interested in the overall performance of its students in the academic year 2020/2021. There were 1460 students registered for this academic year. The University decides to select a sample of 150 students from each of the 5 faculties- Science, Medicine, Law, Social Science and Humanities in proportion to the number of students in each faculty. i. Identify the population of interest for this scenario. ii. Identify the sampling technique used by the researcher. iii. State one advantage and one disadvantage of the sampling technique described in the given scenario. iv. If the medical faculty has 584 students registered, calculate how many medical students would be part of the sample of 150.

b) The Table below shows the average score of the150 students sampled from the University of the East Europe in the academic year 2020/2021. Score (out of 100) Number of students 40-44 19 45-59 32 60-64 49 65-69 29 70-74 21 i. calculate the mean score of the students ii. calculate the modal score iii. calculate the median score iv. Use your results above to comment on the shape of the distribution. Give a reason for your answer.

Question 2 _____________________________________________________________________________ a) A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, = 14.9 mm, and a standard deviation, s = 1.33 mm. A test was carried out at the 5% level of significance to determine whether the machine is in good working order. Assume that the diameter of the disc follows a normal distribution.

i. State, in symbols, the null and alternate hypotheses for this test. ii. State, with reasons, whether a t-test or a z-test will be appropriate. iii. (Determine the rejection region(s) of the test. iv. Calculate the value of the test statistic. v. State, with reason, a valid conclusion for the test.

b) Persons who visit the restroom of a certain fast-food outlet were asked to state their opinion of the quality of the restroom facilities, The following tables show the responses from a sample of 100 persons.

Gender of Respondent Totals Male Female Quality of Facilities Above Average 8 7 15 Average 26 24 50 Below Average 7 28 35 Totals 41 59 100 A 2 test is carried out to determine whether there is an association between the gender of persons and their opinion. i) State appropriate null and alternative hypotheses ii) Determine the critical region of the test at the 1% level of significance iii) Calculate the value of your test Statistic iv) What is your conclusion for this test. Give a reason for your answer Question 3 _____________________________________________________________________________ Bluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sq ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract of the output obtained: The regression equation is = + + + Predictor Coef SE Coef T P Constant 37718 14177 2.66 ** Bedrooms 2306 6994 0.33 0.742 House Size 74.3 52.98 * 0.164 Lot Size -4.36 17.02 -0.26 0.798

S= 25023 R-Sq=56.0% R-Sq(adj)=54.6%

Source DF SS MS F P Regression 3 76501718347 25500572782 *** **** Residual Error 96 60109046053 626135896 Total 99 a) Write out the regression equation. b) Fill in the missing values *, **, *** and ****. c) Use the p-value approach to determine if is significant at the 5% significance level d) Is significantly different from -0.5? e) Perform the F test at the 1% level, making sure to state the null and alternative hypotheses. f) Give an interpretation to the term "R-sq" and comment on its value.