Question

The equatorial radius of the planet Jupiter is measured 40 times by a process that is practically free of bias. These measurements average is 71492 kilometers with a standard deviation of 28 kilometers. Find a 93% confidence interval for the equatorial radius of Jupiter

Answer 1

Answer:

The 93% confidence interval for the equatorial radius of Jupiter is between 71484 km and 71500 km.

Step-by-step explanation:

Sample size of 30 or larger, so we can use the normal distribution to find the confidence interval.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.93}{2} = 0.035$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.035 = 0.965$, so $z = 1.81$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.81*\frac{28}{\sqrt{40}} = 8$

The lower end of the interval is the sample mean subtracted by M. So it is 71492 - 8 = 71484 km.

The upper end of the interval is the sample mean added to M. So it is 71492 + 8 = 71500 km.

The 93% confidence interval for the equatorial radius of Jupiter is between 71484 km and 71500 km.