EXERCISE (MTH 3003-PJJ)
- Independent random samples of and observations were selected from binomial populations 1 and 2, and and successes were observed. Let denote and as a proportion for population 1 and 2 respectively.
(a)Find the point estimator for
(b)Construct a 90%, 95% and 98% confidence interval for
(c)What conclusion would you make based on confidence interval in (b)
2.A random sample of observations from a quantitative population producesand. Let denote as a population mean. Suppose the interest is to test whether is different from 0.
(a)What are the suitable hypotheses to be tested?
(b)Calculate the test statistic value
(c)using 5% level of significance, conduct the test. State your rejection region, decision and conclusion.
3.A company sent 7 of its employees to attend a course in building self-confidence. Their confidence level then evaluated before and after attending this course. The summary of data were as follows: and Suppose you wish to detect
(a)What are the appropriate hypotheses to be tested?
(b)Calculate the test statistic value
(c)Find the rejection region for testing whether there is a difference between the population means at 5% significance level.
4.A sample of 18 observations selected from a normally distributed population produced a sample variance of 4.6.
(a)Write the null and alternative hypotheses to test whether the population variance is different from 2.2.
(b)Suppose you wish to conduct the test in (a). What is the value of test statistic?
5.The height of two rivers (in meter) in Selangor was recorded for a period of 10 days. The following information was obtained:
(a)State the null and alternative hypotheses in order to test whether is larger than
(b)Calculate the value of the test statistic.
(c)Using 5% level of significance, test whether is larger than. State your rejection region, decision and conclusion.
6.A dietitian wanted to test three different diet programs to find out if the mean weight loss for each of these diet programs is the same. She randomly selected 24 overweight persons, divided them into three groups of equal size, and put each group on one of the three diet programs. The partial ANOVA table for the data on weight loss is given below:
Source / Degree of Freedom / Sum of Squares / Mean Square / F valueTreatment / A / 30.083 / E / G
Error / B / D / F
Total / C / 117.958
(a)Determine the values of A, B, C, D, E, F and G.
(b)State the null and alternative hypotheses.
(c)Do the data provide sufficient evidence to indicate differences among the mean weight loss by all persons on each of these three diet programs at a significance level of 5%? State your rejection region, decision and conclusion.
7.A study is conducted to compare the hardness of certain material produced at three different temperature setting A, B and C. Because there might be variability from the different machines used to produce the materials, the researcher decided to use randomized block design, with the machine considered as block. The results of the reading on hardness scale of material produced are as follows:
Block / A / B / C / Total1 / 8 / 0 / 3 / 11
2 / 10 / 5 / 9 / 24
3 / 3 / 2 / 5 / 10
4 / 6 / 8 / 6 / 20
Total / 27 / 15 / 23 / 65
(a)Calculate the value of total sum of squares (Total SS), sum of squares for treatments (SST), sum of squares for blocks (SSB) and sum of squares for error (SSE) for the above data.
(b)Construct the ANOVA table, showing all sums of squares, degree of freedom, mean squares and F-values.
8.You work for an insurance company and are studying the relationship between types of crashes and the vehicles involved. As part of your study, you randomly select 3207 vehicle crashes and organize the resulting data as shown in the contingency table. At can you conclude that the type of crash depends on the type of vehicle?
VehicleType of crash / Car / Lorry / Van
Single-vehicle / 895 / 493 / 45
Multiple-vehicle / 1400 / 336 / 38
Conduct the appropriate analysis to answer the following questions.
(a)Calculate the expected frequency for each cell
(b)Calculate the test statistic,
(c)Using 5% level of significance, testswhether the type of crash is independent on the type of vehicle.State your rejection region, decision and conclusion
9.A medical doctor wishes to examine the linear relationship between the arm span (x) and the height (y) for patients. The summaries of data are as follows:
(a)Find the estimated linear regression line
(b)Estimate the height for a particular patient who the measures of arm span is 62
(c)Calculate the coefficient of correlation,
(d)Test at whether the true correlation coefficient, is positive
LIST OF FORMULAE
/ Linear Regression and CorrelationMTH3003 (PJJ) – SEM 2 2015/2016