Questions: Flavia was curious if a sample first quartile (or Q1) was an unbiased estimator of a population first quartile. She started with a large normally distributed population of test scores whose first quartile was Q1=70 points. She then took a random sample of 6 tests and calculated the first quartile of the sample. She replaced those tests and repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each dot represents the first quartile from a sample of 6 tests. Based on these results, does sample first quartile appear to be a biased or unbiased estimator of population first quartile? Hint: The population first quartile is 70. Choose 1 answer: (4) Sample first quartile appears to be a biased estimator since it consistently underestimated the population first quartile. (0) Sample first quartile appears to be a biased estimator since it consistently overestimated the population first quartile. (c) Sample first quartile appears to be an unbiased estimator of the population first quartile.

Flavia was curious if a sample first quartile (or Q1) was an unbiased estimator of a population first quartile. She started with a large normally distributed population of test scores whose first quartile was Q1=70 points. She then took a random sample of 6 tests and calculated the first quartile of the sample. She replaced those tests and repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each dot represents the first quartile from a sample of 6 tests. Based on these results, does sample first quartile appear to be a biased or unbiased estimator of population first quartile? Hint: The population first quartile is 70. Choose 1 answer: (4) Sample first quartile appears to be a biased estimator since it consistently underestimated the population first quartile. (0) Sample first quartile appears to be a biased estimator since it consistently overestimated the population first quartile. (c) Sample first quartile appears to be an unbiased estimator of the population first quartile.
Transcript text: Flavia was curious if a sample first quartile (or $Q_{1}$ ) was an unblased estimator of a population first quartile. She started with a large normally distributed population of test scores whose first quartile was $Q_{1}=70$ points. She then took a random sample of 6 tests and calculated the first quartile of the sample. She replaced those tests and repeated this process for a total of 50 triats. Her results are summarked in the dotplot below, where each dot represents the first quartile from a sample of 6 tests. Based on these results, does sample first quartile appear to be a blased or unblased estimator of population first quartile? Hint: The population first quartile is 70 . Choose 1 answer: (4) Sample first quartile appears to be a blased estimator since it consistently underestimated the population first quartile. (0) Sample first quartile appears to be a blased estimator since it consistently overestimated the population first quartile. (c) Sample first quartile appears to be an unblased estimator of the population first quartile.
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Solution

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Solution Steps

Step 1: Understand the Problem

Flavia is testing if the sample first quartile (\(Q_1\)) is an unbiased estimator of the population first quartile. The population first quartile is given as 70. She took 50 samples of size 6 and calculated the first quartile for each sample. The results are shown in a dot plot.

Step 2: Analyze the Dot Plot

The dot plot shows the distribution of the sample first quartiles. Each dot represents the first quartile from a sample of 6 tests. The x-axis ranges from 60 to 80.

Step 3: Compare Sample Quartiles to Population Quartile

The population first quartile is 70. To determine if the sample first quartile is an unbiased estimator, we need to see if the sample quartiles are centered around 70.

Final Answer

The sample first quartiles are mostly centered around 70, with a roughly symmetric distribution around this value. Therefore, the sample first quartile appears to be an unbiased estimator of the population first quartile.

Answer: C. Sample first quartile appears to be an unbiased estimator of the population first quartile.

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