Question 2

Do the calculations 'by hand'

(using a calculator), showing your working.

A newspaper headline includes the following statement "average range for electric vehicles now 225 miles". In this context, range refers to the distance an electric vehicle can travel before the battery needs to be recharged.

A consumer group decides to check the newspaper's statement by testing 24 of the most popular electric cars on the market. The cars were each fully charged and then driven around a track in the same conditions and at the same speed until the charge was fully depleted. The number of completed miles travelled when the battery ran out was recorded.

The results are summarised in Table 2.

Table 2 Summary statistics for the range (in miles) of electric cars tested

Sample size	Mean	Standard deviation
24	208	32

• (a) What is the most appropriate version of the t-test if you want to test the null hypothesis that the underlying population mean distance an electric vehicle can travel before the battery needs to be recharged is what the newspaper headline claims it to be and the alternative hypothesis is that the underlying population mean distance an electric vehicle can travel before the battery needs to be recharged is not what the newspaper headline claims it to be? Justify your choice.
• (b) What are the number of degrees of freedom and the 5% critical value for the most appropriate t-test applied to these data?
• (c) Without using Minitab, calculate a 95% confidence interval for the population mean distance an electric vehicle can travel before the battery needs to be recharged. Your answer should be rounded to the nearest whole number.
• (d) Based on your calculated 95% confidence interval, is it plausible that the underlying population mean distance an electric vehicle can travel before the battery needs to be recharged is 225 miles as claimed by the newspaper headline? Justify your answer.