Question

question 28 (3 points)
a 95% confidence interval for the mean weight of apples from an orchard is (150 grams, 170 grams). which of the following is the best interpretation of this interval?
we are 95% confident that the true mean weight of all apples from the orchard is between 150 and 170 grams.
there is a 95% chance that a randomly - selected apple will weigh between 150 and 170 grams.
the mean weight of the sampled apples is between 150 and 170 grams.
95% of all apples weigh between 150 and 170 grams.
question 29 (3 points)
the test scores of a class are as follows: 85, 90, 78, 92, 88, 76, 95, 89, 92, 84. what is the mean score and how does it help in understanding the overall performance of the class?
the mean is 86.9. the mean score gives an idea of the average performance of the class.
the mean is 88.5. the mean score gives the midpoint of the test grades.
the mean is 92. the mean score gives an idea of the most recurring grades in the class.

Explanation:

Question 28

A confidence interval is an interval estimate of a population parameter. A 95% confidence interval for the population mean implies that if we were to take many samples and construct confidence intervals in the same way, about 95% of them would contain the true population mean. It is not about the probability of an individual value or the sample - mean in the same sense.

Step1: Calculate the sum of scores

$85 + 90+78 + 92+88+76+95+89+92+84=869$

Step2: Calculate the number of scores

There are $n = 10$ scores.

Step3: Calculate the mean

The mean $\bar{x}=\frac{869}{10}=86.9$. The mean gives an idea of the average performance of the class.

Answer:

We are 95% confident that the true mean weight of all apples from the orchard is between 150 and 170 grams.

Question 29