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**Statistical Methods Questions Set**

ORDER # | 100406 |

PAPER TYPE | MATH PROBLEMS |

WRITING LEVEL | MASTERS |

WRITING STYLE | HARVARD |

# OF SOURCES | N/A |

# OF PAGES & WORD COUNT | 5 ≈ 1375 WORDS |

**Statistical Methods Questions Set**

**State your hypothesis, test statistic and decision rules.**

**Insert all workings out – either written beneath main answers, copy and pasted through excel or excel screenshots. Workings out must be included. Word count does not include workings out or tables.**

**Clearly state your conclusions**

**Question A1**

**A) Treaddur Bay Sea View hotel has surveyed guests at checkout. A section of the**

**survey asked if their experience was better than expected, as expected, or less than **

**expected. The results showed 4% did not complete the survey, 26% said it was less. **

**than expected and 65% said it was as expected.**

**i) If you selected a survey at random what is the probability that it would score.**

**better than expected?**

**ii) If you selected a survey at random what is the probability that it would score.**

**at least that their expectations were met.**

**Explain your answers in both words and numbers.**

**B) There are numerous ways in which sampling can be conducted. Name three and**

**identify their strengths and weaknesses.**

**Question A2**

**A) To create a better Covid risk assessment for its 3500 employees, Anglesey County**

**council needed to estimate their mean age, simple random sample of 35 records are. **

**selected.**

** **

**i) Do you need to use the finite correction factor? Explain your answer.**

**ii) If the population 𝜎 is 8.5 years? Compute the standard error with and without**

**the population finite factor. Comment on your findings.**

**iii)What proportion of the sample has a mean age within plus ± two years of the?**

**population means?**

**B) Which the UK consumer organisation conducted a survey to calculate the average**

**cost of diesel fuel. They found the average cost per litre was £1.265 with a standard. **

**deviation of 0.14. **

** **

**What sample size would be required for a follow up survey that had each of the**

**following margin of error at a 95% confidence interval.**

**10 p****5p****2p**

**Explain your findings in terms of sample size and margin of error.**

**Question A3**

**A) In Britain, the average car insurance premium is £460 per annum. Would you expect it?**

**to be cheaper in rural Wales? To test that a sample of twenty-five motorists in south **

**Gwynedd were asked how much they pay for insurance in 2020. The mean cost of **

**£440 and a standard deviation of £45. **

**Construct a hypothesis test and report on your findings. Use a significance value of 0.05.**

**B) The Office of National statistics report that the average duration of unemployment**

**for working age adults was twenty weeks in the North of England, with a population **

**standard deviation of five weeks. This compared to a duration of sixteen weeks, with **

**a population standard deviation of six weeks in the South of England. Assume a **

**sample size of one hundred in both regions. **

**What is the probability of a sample of?**

**one hundred having a mean within one week of the population mean for:**

**a) the North of England, and**

**b) the South of England?**

**Comment on your findings**

**Question B1**

** Farmers supplies Cymru are reviewing their business expenditure to assess the effects of Brexit on their sales. They have produced an estimated regression equation relating their sales to the **

**amount of stock they hold, and their advertising expenditure. This equation was based on data. **

**obtained from ten depots throughout Wales. **

**Y= 20 +11×1 + 6×2**

**Where x1 = stock costs (in £1000)**

**x2= advertising cost (in £1000)**

**y = sales in £**

**The data gave an SST = 8000, and SSR = 6000**

**a) Estimate the sales if Farmers supplies Cymru spend £25,000 on stock, and**

**£15,000 on advertising.**

**b) Explain what b1 and b2 mean in relation to Farmers Supplies Cymru**

**c) Using the estimated regression equation, calculate R2**

**d) Calculate the Ra2**

**e) Explain how well the model accounts for the variability in the data.**

**f) Calculate the SSE, MSE and MSR**

**g) Using an F test and 0.05 level of significance, determine whether there is a**

**relationship among the variables.**

**Question B2**

**The following data was collected on a Time series.**

Week | 1 | 2 | 3 | 4 | 5 | 6 |

Value | 18 | 13 | 16 | 11 | 17 | 14 |

** **

**Forecast the next week value, using the most recent value method. Then calculate the following. **

**measures of accuracy:**

**a) Mean absolute error****b) Mean squared error****c) Mean absolute percentage error****d) Forecast the value for week 7**

**Repeat the same exercise but use the average of all data as the forecast for the next week.**

**Then compare the results of the two forecast methods, which method gave the more.**

**accurate forecast?**

**State your hypothesis, test statistic and decision rules.**

**Insert all workings out – either written beneath main answers, copy and pasted through excel or excel screenshots.**

**Workings out must be included.**

**Word count does not include workings out or tables.**

**Clearly state your conclusions**

**Fully explain your findings**

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