a) A highway patrol officer believes that the average speed of cars traveling over a certain stretch of highway exceeds the posted limit of 55 km/ hr. A random sample of 10 cars had their speeds...

a)
A highway patrol officer believes that the average speed of cars traveling over a certain stretch of highway exceeds the posted limit of 55 km/ hr. A random sample of 10 cars had their speeds measured by radar. The results in Km / hr are as follows:

71, 53, 62, 49, 59, 52, 58, 61, 85, 55

Do these data provide sufficient evidence to support the highway patrol belief, at the 10% level of significance?

b)
Measurements are made on a random sample of 100 components drawn from a population of size 1546 and having a standard deviation of 2.93 mm. The mean measurement of the components in the sample is 67.45 mm. Determine:

i.
The standard error of the mean

ii.
The 99% confidence limits for an estimate of the mean of the population