Unit: Quantitative Analysis
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Login to Access| University | Number of students before advertisement | Number of students after advertisement |
| A | 170 | 180 |
| B | 145 | 151 |
| C | 150 | 143 |
| D | 170 | 177 |
| E | 172 | 178 |
| F | 164 | 167 |
| Regression statistics: | |
| Parameter | Output |
| Multiple R | 0.981542 |
| R square | A? |
| Adjusted R square | 0.955684 |
| Standard error | 24.137620 |
| Observations | 10 |
| ANOVA Table: | |||||
| Source | d.f | SS | MS | F | Significance |
| Regression | 2 | 254,600.40 | C = ? | D = ? | 0.000089 |
| Residual | 7 | B=? | 3,456.21 | ||
| Total | 9 | 263,000 |
| Regression coefficients: | ||||||
| Variable | Coefficient | Standard error | t-statics | P value | Lower 95% | Upper 95% |
| Intercept | 480.32 | 30.1175 | E = ? | 0.000012 | 410.28 | 550.36 |
| Service hours (\(X_1\)) | F= ? | 4.9162 | 5.847 | 0.000095 | 22.32 | 35.18 |
| Replacement parts (\(X_2\)) | 15.60 | 3.2453 | 48.08 | 0.000231 | 10.32 | 20.88 |
| Accounting Department | Marketing Department | |
| Number of employees | 40 | 50 |
| Average monthly salary | Sh.120,000 | Sh.130,000 |
| Standard deviation | Sh.10,000 | Sh.12,000 |
A sample of 36 packets of sugar has an average weight of 500 grams with a standard deviation of 25 grams.
Required:
Test at a 5% significance level if there is sufficient evidence to reject the manufacturers claim
| Month | July | August | September | October | November | December |
| Number of Companies | 326 | 290 | 306 | 260 | 355 | 365 |
\(H_1: \mu \neq 400\)
For a random sample of 12 observations, the sample mean was 407 and the sample standard deviation was 6.
Required:
Using a significance level of 0.1, advise whether the null hypothesis should be accepted or rejected
Required:
On the basis of a sample of 200 residents:
(i) Construct a 95% confidence interval for the monthly rent paid.
(ii) Test the hypothesis that the amount paid in monthly rent is Sh.20,000 at a 5% significance level
| Day of the week | Number of employees |
| Monday | 207 |
| Tuesday | 185 |
| Wednesday | 203 |
| Thursday | 180 |
| Friday | 225 |
| Total | 1,000 |
Required:
(i) The interval within which the population mean should fall at 95% level of confidence.
(ii) The sample size of invoices that would result in a 99% confidence level of the interval obtained in (a) (i) above.
| Won | Defeated | Drawn | |
| Adopted strategy K | 130 | 20 | 60 |
| Adopted strategy P | 110 | 30 | 50 |
| Brand A | Brand B | |
| Mean life (days) | 1,730 | 1,684 |
| Standard deviation (in days) | 102 | 108 |
| Sample size | 200 | 200 |
(i) Type 1 and Type II errors.
(ii) One-tail test and two-tail test.
(iii) Normal distribution and t-distribution.
| Region | Sales before promotional campaign "Sh.million" | Sales after promotional campaign "Sh.million" |
| 1 | 53 | 58 |
| 2 | 28 | 29 |
| 3 | 31 | 30 |
| 4 | 48 | 50 |
| 5 | 50 | 50 |
| 6 | 42 | 45 |
| 7 | 63 | 59 |
| 8 | 40 | 36 |
| 9 | 25 | 22 |
| 10 | 30 | 28 |
| Classes | ||
| Day | Evening | |
| Number of students | 13 | 15 |
| Average test mark (%) | 45 | 55 |
| Standard deviation (%) | 4 | 5 |
| Department P | Department Q | |
| Number of employees | 29 | 24 |
| Average monthly salary | Sh.260,000 | Sh.310,000 |
| Standard deviation | Sh.25,000 | Sh.30,000 |
| Outlet | Monthly mean sales (Sh."000") | Standard deviation (Sh."000") | Sample size |
| A | 795 | 50 | 200 |
| B | 810 | 70 | 175 |
| Component X | Component Y | |
| Mean life in hours | 1,600 | 1,528 |
| Standard deviation in hours | 132 | 149 |
| Sample size | 120 | 110 |
| College | Number of students before advertisement | Number of students after advertisement |
| 1 | 165 | 170 |
| 2 | 140 | 141 |
| 3 | 143 | 142 |
| 4 | 160 | 167 |
| 5 | 162 | 168 |
| 6 | 154 | 157 |