Example 1 - a. quantitative (continuous), ratio; b. qualitative, nominal; c. qualitative, ordinal; d. quantitative (discrete), interval; qualitative, ordinal

Example 2 - a. False (inferential statistics); b. False (nominal, ordinal, interval, ratio); 1c. False (100 is sample)

Example 3 - Nominal

Example  4 - Ratio or interval

Example 5 - Ordinal, because we can rank r order the responses

Example 6 - Quantitative (discrete)

Example 7 - Ratio

(There are no examples 1 to 4)

Example 5 - VADS a. 23.9, b. parameter because it includes all calls in the first 7 days in May; Giant a. 10.73, b. statistics because it is a sample of workers

Example 6 - a. 2.5; b. Yes, she will be admitted.

Example 7 - a. 9.9%; b. 10.1%; c. GM is always less than arithmetic mean

Example 8 - GM (public college) = 5.66%, GM (private college) = 5.52%; The rates of increase are about the same. 

Example 9 - a. 24; The most frequent number of years a person works before retiring is 24 years; b. 19.91; The average number of years that a person works before retiring is about 20 years; c. 21; Half of the workers work less than 21 years before retiring and the other half of the workers work more than 21 years before retiring.

Example 10 - a. 46.8, 42.5, 40; b. The admission price for one-day tickets is slightly skewed to the right because the mean is slightly greater than the median. 

Example 11 - Mean (Machine A) = 200, SD (Machine A) = 2.50; Mean (Machine B) = 200, SD (Machine B) = 5.16; Since the standard deviation for Machine A is smaller, it indicates that Machine A is more reliable than Machine B.

Example 12 - Using the Empirical rule, approximately 95% of the people are between 16 to 64 years old. 

Example 13 - a. Curve B; b. 40; between 35 and 45.

Example 14 - a. To find k, if we use the lower limit: x ̅-k. s=600, solve for k=5, thus at least 1-1/k2=1-1/25=96%;  b. (96/100) x 75 = 72 part-time assistants.

Example 15 -  Between 93.52 and 128.48

Example 16 - sk = -0.51; The distribution is slightly skewed to the left

Example 1 - 100, 112, 125, 140, 180, 200; Price index for 1998 is 112, so the book price in 1998 has increased by 12%.

Example 2 - 124.39; The prices of machines have increased by 24.39% over the period 1996 to 2001

Example 3 - a. 83.3, 120, 90, 166.67; b. 128.8; c. 98.4, The price of vegetables has reduced by 1.6% over the least four years; d. 107.03, The price of vegetables has increased by 7.03% over the last four years; e. 102.62

Example 4 - 

Example 1 - a) 0.08, 0.152, 0.212, 0.18, 0.16, 0.052, 0.02, 0.144; b) 4.144, 2.091; c) RM 11.53, RM 5.01

Example 2 - a) 0.3; b) 0.5

Example 3 - 2.8 days, 1.3 days

Example 4 - a) 0.2059; b) 0.0105; c) 13.5; d) 1.35, 1.161

Example 5 - a) 0.2311; b) 0.0138; c) 0.1678; d) 3.6

Example 6 - a) 0.168; b) 0.837; c) 0.03; d) 3.5, 1.025

Example 7 - a) 0.1667; b) 0.9838

Example 8 - a) 0.223; b) 0.3971

Example 9 - a) 1.5; b i) 0.2231; b ii) 0.047; c) 0.442; d) 0.0497 (4 decimal spaces)

Example 10 - a) 0.055; b) 0.666

Example 11 - a) 490 and 510; b) 480 and 520; c) 470 and 530

Example 12 - a) 1.25; b) -1.25

Example 13 - a) 0.7745; b) 0.5987

Example 14 - a) 0.1587; b) 0.0466; c) 0.2195; d) 0.4967

Example 15 - a) 13.4%; b) 19.65%; c) 45.8%

Example 16 - $ 34,314

Example 17 - 3.10

Example 18 - 0.1038

Example 19 - a) 10 installations; b) 0.1894; c) 0.2981; d) 0.1087

Example 5 - a) Possible answers – simple random sampling, systematic random sampling or stratified random sampling. Reasons will depend on the selected sampling technique; b) Convenience online sampling. Possible flaws: biased results, inability to reach challenging population, question of honesty, survey fraud, especially when there is reward attached to response, misrepresentation of data & incomplete conclusions etc.

Example 6 -  a) 6.5; c) 97.5/15 = 6.5; d) If all possible samples of the same size are selected, the mean of the sampling distribution of the sample mean would be exactly equal with the population mean. However, the dispersion of the sampling distribution of the sample mean (i.e. the standard error) would be narrower/smaller than the population standard deviation. 

Example 7 - a) 0.0228; b) 0.44; c) 0.7852

Example 8 - a) 0.0655; b) 21.46

Example 1 - a) Population  mean is not known. But the best estimate of the population mean is the sample i.e. RM 5,000; b) RM 4869.32, RM 5130.68. Interpret: We are 95% confident that with repeated sampling, the true value of the population mean lies between RM 4869.32 and RM 5130.68; c) RM 4827.98, RM 5172.02. Interpret: We are 99% confident that the true value of the population mean lies between RM 4827.98 and RM 5172.02 with repeated sampling; d) No, because RM 5200 does not fall between the confidence interval of RM 4827.98 and RM 5172.02; e) The confidence interval gets wider as the confidence level gets higher. At 95% confidence level, the difference between the lower and upper limits is 261.36 while at the 99% confidence level,  the difference is 344.04; e) Higher confidence level provides more reliability, however, it brings less precision. 

Example 2 - a) 3.53 and 1.55; b) No, because 4 is not within the confidence interval.

Example 3 - a) Population mean is not known. Therefore, the best estimate of this value is the sample mean, which is 60; b) We need to use the t-distribution because 1. population standard deviation is unknown and 2. the sample size is small (n<=30). We assume that the population is normally distributed; c) t = 1.753; d) Between 51.24 and 68.77; e) Yes

Example 4 - 3.77% to 8.7%; We are 95% confident that the true value of the population proportion lies between 3.77% and 8.7%.

Example 5 - a) Between 0.245 and 0.455; b) Between 0.352 and 0.548; c) There is no sufficient evidence that the sales of Upin & Ipin comic is higher than the sales of Kuntum magazine because their confidence intervals overlap with one another. (Try sketching both the C.I. You can only say something is higher than another if there is no overlap)

Example 6 - 0.4553, 0.7447 (make sure the FPC condition is met first)

Example 7 - 2.85, 9.15 error per purchase order (make sure the FPC condition is met first)

Example 8 - Sample size should be 25 boxes

Example 9 - a) 5718 people; b) To reduce the sample size, we can either (i) reduce the level of confidence or (ii) increase the margin of error. In this case, we choose to increase the error from 1% to 5% because the confidence level is already "low" at 90%; c) New sample size is 229.

Example 1 - Two-tailed test; Test statistic =-1.77; Do not reject Ho. There is enough sample evidence to suggest that the mean waiting time is 3 minutes. 

Example 2 - One-tailed test; Test statistic = -1.77; Reject Ho. There is enough sample evidence to suggest that the mean waiting time is less than 3 minutes. 

Example 3 - a) p-value is 0.0768; Do not reject Ho; b) p-value is 0.0384; Reject Ho

Example 4 - One-tailed test; Test statistic = -3.084; Reject Ho. Conclude that the assembly time using the new method is faster; p-value is between 0.0005 and 0.005.

Example 5 - One-tailed test; Test statistic = 1.95; Reject Ho, and conclude that on average, people take longer coffee breaks.

Example 6 - xbar = 77.3; sd = 11.46; Two-tailed test; standard error = 2.01, z-test statistic = 1.84 (use Z if we assume that the teacher's collection of final grades in the last 10 years is the population standard deviation); critical value = +/- 1.96; Do not reject Ho and conclude that this year's final grades do not differ significantly from previous years; p-value = 0.0658 is greater than 0.05, we fail to reject the null hypothesis. 

Example 7 - Two-tailed test; Test statistic = -1.53; Do not reject Ho, conclude that there is no difference in the mean number of KM travelled per month between Gombak and Kuantan employees. 

Example 8 - One-tailed test; Test statistic = 2.09; Reject Ho and conclude that union nurses earn more than non-union nurses; p-value is 0.0183

Example 9 - One-tailed test; Estimate of the pooled variance = 278.69; Test statistic =1.95; Do not reject Ho, and conclude there is no difference in the mean amount of time watching TV together between single-earner and dual-earner couples. 

Example 10 - Two-tailed test; Estimate of the pooled variance = 254.001; Test statistic = -3.045; Reject Ho. This indicates that the mean weekly sales of ABC Cola are different between normal shelves and end-aisles; p-value is between 0.01 and 0.001 (very small).

Example 11 - One-tailed test; dbar = 2; Sd = 2.082; Test statistic = 2.542; critical value = 1.943; Reject Ho and conclude that the training was effective.

Example 12 - One-tailed test; dbar = 3.625; Sd = 4.8385; Test statistic = 2.12; Do not reject Ho and conclude that the number of crimes has not decreased since the launch of the program. 

Example 13 - Two-tailed test; dbar = 0.3; Sd = 0.335; Test statistic = 2.20; Do not reject Ho and conclude that the average completion times do not differ with one another; p-value is between 5% to 10%.

Example 1 - 9.78

Example 2 - Test statistic = 3.36; Reject Ho and conclude that there is more variation in the processing time of the new machine.

Example 3 - This is a one-tailed test so significance level becomes .05; Test statistic = 1.44; Critical value is 3.11 (found by  taking the average of the values 3.14 and 3.07 belonging to 10 and 12 when you connect them with df (denominator) 9); Do not reject Ho and conclude that there is no difference in the variation in the listening habits for men and women. 

Example 4 - SS Total = 2872; SSE = 2782; F-test statistic = 0.194; Do not reject Ho and conclude that there is sufficient evidence to suggest that there is no significant difference in the average scores of the students from the three universities. 

Example 5 - SST Total = 16,350; SSE = 7600; F-test statistic = 6.14; Reject Ho and conclude that there is a significant difference among the employees' outputs assigned to the different programs. 

Example 6 - a) df = 2,9,11; SSE = 6322; MST == 4776.46; MSE = 702.44; F = 6.8; b) Reject Ho and conclude that there is a significant difference in the averages of studying time for the three groups.

Example 1 - Test statistic = -0.4; Do not reject Ho and conclude that the proportion of students who has changed their major has not changed.

Example 2 - Test statistic = 2; Do not reject Ho and conclude that the proportion of students with jobs is not larger.

Example 3 - Pc = 0.59; Test statistic = 12.6; Reject Ho and conclude that the proportion of women who think men are thoughtful has declined.

Example 4 - Test statistic = 3.85; Reject the Ho and conclude that the proportion of men who prefer cone is different from the proportion of women who prefer cones in the population. p-value = 0.0001 (< .05) so reject the Ho.

Example 5 - (Note: There was a typo in your lecture note. E is 210. But feel free to redo the whole problem with 120); Test statistic = 14.62; Reject Ho and conclude that there is enough evidence to suggest that customers do not prefer each of the five stores equally.

Example 6 - Test statistic = 0.875; Do not reject Ho and conclude that the the pattern has not changed.

Example 7 - Test statistic = 6.6462; Reject Ho and conclude that anxiety is related to the frequent flier status. (No need to find p-value)

Example 8 - Test statistic = 2.191; Do not reject Ho and conclude that there is no relationship between job pressure and age. 

Example 9 - Test statistic = 16.422; Reject Ho and conclude that there is an association between gender and job category in the supermarket chain.