- 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:
<u>Where:</u>
- is the standard deviation.
Substituting the given parameters into the formula, we have;
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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