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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.

Respuesta :

Answer:

B. 65.00 ± 2.35.

Step-by-step explanation:

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

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

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

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

The confidence interval has the following format:

[tex]x¯ \pm z\frac{\sigma}{\sqrt{n}}[/tex]

So

[tex]65 \pm 1.96\frac{2.4}{\sqrt{4}} = 65 \pm 2.35[/tex]

So the correct answer is:

B. 65.00 ± 2.35.

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