(1)In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company wants to perform a test to determine whether this average duration of long distance calls has changed. Fifty calls, originating from the town, was randomly selected and the following summary minutes. ∑ ? = 205 ∑(? − ?̅)2 = 56.43 a) Calculate the sample mean, ?̅. b) Calculate the sample standard deviation c) Using the p value approach at the 1% level of significance, test whether the mean duration of long-distance calls from the town had increased. d) Construct the 99% confidence interval for the population mean duration of the long-distance calls from the town. (2) A researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+???? Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev y-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 Oil 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 * 0.0057 FDI -396.99 160.66 -2.471 ** S = 2.45 R – sq = 96.3% R – sq (adj) = 95.3% Analysis of Variance Source DF SS MS F P Regression 3 1991.31 663.77 ? ?? Error 12 77.4 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ‘*’, ‘**’, ‘?’and ‘??’ d) Hence test whether ? is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis f) Given an interpretation of the term “R-sq” and comment on its value.
Answer questions 1 and 2 completely.
(1)In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company wants to perform a test to determine whether this average duration of long distance calls has changed. Fifty calls, originating from the town, was randomly selected and the following summary minutes.
∑ ? = 205 ∑(? − ?̅)2 = 56.43
a) Calculate the sample
b) Calculate the sample standard deviation
c) Using the p value approach at the 1% level of significance, test whether the mean duration of long-distance calls from the town had increased.
d) Construct the 99% confidence interval for the population mean duration of the long-distance calls from the town.
(2) A researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016:
??=?+????+????+????
Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:
| Predictor | Coef | StDev | y-ratio | p-value |
| Constant | 5491.38 | 2508.81 | 2.1888 | 0.0491 |
| Oil | 85.39 | 18.46 | 4.626 | 0.0006 |
| EXP | -377.08 | 112.19 | * | 0.0057 |
| FDI | -396.99 | 160.66 | -2.471 | ** |
S = 2.45 R – sq = 96.3% R – sq (adj) = 95.3%
Analysis of Variance
| Source | DF | SS | MS | F | P |
| Regression | 3 | 1991.31 | 663.77 | ? | ?? |
| Error | 12 | 77.4 | 6.45 | ||
| Total | 15 |
a) What is dependent and independent variables?
b) Fully write out the regression equation
c) Fill in the missing values ‘*’, ‘**’, ‘?’and ‘??’
d) Hence test whether ? is significant. Give reasons for your answer.
e) Perform the F Test making sure to state the null and alternative hypothesis
f) Given an interpretation of the term “R-sq” and comment on its value.
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