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3 years ago

PLEASE ANSWER i WILL PUT MOST BRAINLIEST!

Mathematics

1 answer:

galina1969 [7]3 years ago

4 0

Answer:

The correct option is;

c. Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.

Step-by-step explanation:

Here we have the values

μ = 275 mL

275.4

276.8

273.9

275

275.8

275.9

276.1

Sum = 1928.9

Mean (Average), = 275.5571429

Standard deviation, s = 0.921696159

We put the null hypothesis as H₀: μ₁ = μ₂

Therefore, the alternative becomes Hₐ: μ₁ ≠ μ₂

The t-test formula is as follows;

$t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}$

Plugging in the values, we have,

Test statistic = 1.599292

$t_{\alpha /2}$ at 7 - 1 degrees of freedom and α = 0.05 = ±2.446912

Our p-value from the the test statistic = 0.1608723≈ 0.1609

Therefore since the p-value = 0.1609 > α = 0.05, we fail to reject our null hypothesis, hence the evidence suggests that the mean does not differ from 275 mL.

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1. Let us proof that √3 is an irrational number, using <em>reductio ad absurdum</em>. Assume that $\sqrt{3}=\frac{m}{n}$ where $m$ and $n$ are non negative integers, and the fraction $\frac{m}{n}$ is irreducible, i.e., the numbers $m$ and $n$ have no common factors.

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