Question

The time (in days) until maturity of a certain variety of tomato plant is Normally distributed, with mean µμ and standard deviation σ=2.4σ=2.4 . I select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields x¯=65x¯=65 . A 95% confidence interval for µμ (in days) is:

A. 65.00 ± 4.70.
B. 65.00 ± 2.35.
C. 65.00 ± 3.95.
D. 65.00 ± 1.97.

Answer 1

B. 65.00 ± 2.35.

Explanation:

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

`\alpha = (1-0.95)/(2) = 0.025`

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
`1-0.025 = 0.975`, so
`z = 1.96`

The confidence interval has the following format:

`x¯ \pm z(\sigma)/(√(n))`

So

`65 \pm 1.96(2.4)/(√(4)) = 65 \pm 2.35`

So the correct answer is:

B. 65.00 ± 2.35.