A manufacturer claims that a model of electric scooter has a battery charging time of 150 minutes (i.e. 2.5 hours). In o

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A manufacturer claims that a model of electric scooter has a
battery charging time of 150 minutes (i.e. 2.5 hours). In order to
test this claim, 22 electric scooters of that model were charged
from empty to full battery. The length of time for each scooter to
charge fully was recorded in minutes. The results are summarised in
Table 2. Table 2 Summary statistics for the battery charging time
(in minutes) of a model of electric scooter Sample size Mean
Standard deviation 22 161 29 (a) What is the most appropriate
version of the t-test if you want to test the null hypothesis that
the underlying population mean battery charging time for this model
of scooter is what the manufacturer claims it to be, and the
alternative hypothesis is that the underlying population mean
battery charging time is not what the manufacturer claims it to be?
Justify your choice. [2] (b) What are the number of degrees of
freedom and the 5% critical value for the most appropriate t-test
applied to these data? [2] (c) Hence calculate a 95% confidence
interval for the population mean battery charging time for this
model of electric scooter. Your answer should be rounded to the
nearest whole number. [3] (d) Based on your calculated 95%
confidence interval, is it plausible that the underlying population
mean battery charging time is 150 minutes as claimed by the
manufacturer? Justify your answer.