- Since the p-value is approximately equal to zero (0), we can conclude that there is sufficient evidence that the true mean height for the baker's loaves of bread is greater than (>) 15 cm.
- Since 2.37 is greater than (>) 1.645, we reject the null hypothesis (H₀) at 5% level of significance. Therefore, we can conclude that the company’s claims are invalid.
<h3>What is a null hypothesis?</h3>
A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
For the baker's claim, the appropriate null and alternative hypotheses would be given by:
H₀: μ ≤ 15
H₁: μ > 15
Since the standard deviation for the height is given, the population would have a normal distribution, and the population standard deviation is given by:
Population standard deviation = σ/√n
Population standard deviation = 0.5/√10
Population standard deviation = 0.16.
For the p-value, we have:
The p-value is the probability that a sample mean would be the same or greater than (≥) 17 cm. Thus, the p-value is given by:
p-value = P(x > 17) ≈ 0.
Since the p-value is approximately equal to zero (0), we can conclude that there is sufficient evidence that the true mean height for the baker's loaves of bread is greater than (>) 15 cm.
Question 3.
For the oil company's claim, the appropriate null and alternative hypotheses would be given by:
H₀: μ = 0.15
H₁: μ > 0.15
<h3>How to calculate value of the z-score?</h3>
The z-score can be calculated by using this formula:
![z=\frac{x\;-\;u}{\frac{\sigma}{\sqrt{n} } }](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx%5C%3B-%5C%3Bu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
<u>Where:</u>
- is the standard deviation.
Substituting the given parameters into the formula, we have;
![z=\frac{0.162\;-\;0.15}{\frac{0.04}{\sqrt{40} } }\\\\z=\frac{0.012}{\frac{0.4}{6.3246 } }](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B0.162%5C%3B-%5C%3B0.15%7D%7B%5Cfrac%7B0.04%7D%7B%5Csqrt%7B40%7D%20%7D%20%7D%5C%5C%5C%5Cz%3D%5Cfrac%7B0.012%7D%7B%5Cfrac%7B0.4%7D%7B6.3246%20%7D%20%7D)
z = 0.012/0.0633
z = 0.190.
From the z-table, a z-score of 0.190 is equal to a p-value of 2.37.
For the critical value, we have:
Critical probability (p*) = 1 - α/2
Critical probability (p*) = 1 - 0.1/2
Critical probability (p*) = 0.95.
Hence, the critical value is Zα/2 equal to 1.645.
Since 2.37 is greater than (>) 1.645, we reject the null hypothesis (H₀) at 5% level of significance. Therefore, we can conclude that the company’s claims are invalid.
Read more on null hypothesis here: brainly.com/question/14913351
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