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Chapter 7: Q 37. (page 462)
More SkittlesWhat sample size would be required to reduce the standard deviation of the sampling distribution to one-half the value you found in Exercise 35(b)? Justify your answer.
Sample size is
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Tall girls? To see if the claim made in Exercise is true at their high school, an Ap Statistics class chooses an SRS of twenty -year-old females at the school and measures their heights. In their sample, the mean height is inches. Does this provide convincing evidence that -year-old females at this school are taller than inches, on average?
a. What is the evidence that the average height of all -year-old females at this school is greater than inches, on average?
b. Provide two explanations for the evidence described in part (a).
We used technology to simulate choosing SRSs of size from a population of three hundred -year-old females whose heights follow a Normal distribution with mean localid="1654113150676" inches and standard deviation inches. The dotplot shows the sample mean height for each of the simulated samples.
c. There is one dot on the graph at . Explain what this value represents.
d. Would it be surprising to get a sample mean of or larger in an SRS of size when inches and inches? Justify your answer.
e. Based on your previous answers, is there convincing evidence that the average height of all -year-old females at this school is greater than inches? Explain your reasoning.
Suppose we select an SRS of size from a large population having proportion p of successes. Let be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of ?
a. 0.01
b. 0.09
c. 0.85
d. 0.975
e. 0.999
What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.
Sample proportions List all possible SRSS of size , calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot. Is the sample proportion an unbiased estimator of the population proportion? Explain your answer.
| COLOR | AGE |
| RED | |
| WHITE | |
| SILVER | |
| RED |
More sample minimums List all possible SRSs of size n=, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dot plot with the same scale as the dot plot in Exercise . How does the variability of this sampling distribution compare with the variability of the sampling distribution from Exercise ? What does this indicate about increasing the sample size?
From exercise:
| Car Number | Color | Age |
| Red | ||
| White | ||
| Silver | ||
| Red |
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