A manufacturer of car batteries claims that the batteries will last, on average, 3 years with a variance of 1 year. If 5 of these batteries have lifetimes of 1.9, 2.4, 3.0, 3.5, and 4.2 years, construct a 95% confidence interval for σ2 and decide if the manufacturer’s claim that σ2 = 1 is valid. Assume the population of battery lives to be approximately normally distributed.

And in order to obtain the confidence interval for the deviation we just take the square root and we got:

Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim

Step-by-step explanation:

Data provided

1.9, 2.4, 3.0, 3.5, and 4.2

We can calculate the sample mean and deviation from this data with these formulas:

And we got:

s=0.903 represent the sample standard deviation

n=5 the sample size

Confidence=95% or 0.95

Confidence interval

We need to begin finding the confidence interval for the population variance is given by:

The degrees of freedom given by:

The Confidence level provided is 0.95 or 95%, the significance is then and , and the critical values for this case are:

And the confidence interval would be:

And in order to obtain the confidence interval for the deviation we just take the square root and we got:

Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim

1760 kilometers

step-by-step explanation:

multiply the amount of time the plane took to travel by it's speed