Statistical Methods Questions Set

Statistical Methods Questions Set

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

1. 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.

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

identify their strengths and weaknesses.

Question A2

1. 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?

1. 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.

1. 10 p
2. 5p
3. 2p

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

Question A3

1. 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.

1. 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:

1. a) the North of England, and

1. 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.

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

measures of accuracy:

1. a) Mean absolute error
2. b) Mean squared error
3. c) Mean absolute percentage error
4. 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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