1. Pooling across all possible samples, the distribution of sample means is call
ID: 3131714 • Letter: 1
Question
1. Pooling across all possible samples, the distribution of sample means is called the sampling distribution of the sample mean. True or False. Why?
2. The standard error of the sample mean is never larger than the standard deviation of the population distribution. True or False. Why?
3. The sampling distribution of the sample mean can be approximated by plotting a histogram of the sample data. True or False. Why?
4. To study the household income in California, the state government hired two companies. Company A randomly selected 1000 families and reported that the mean income was 74000. Company B randomly selected 2000 families and reported that the mean income was 76000. The government officials should consider company B’s result more reliable. True or False. Why?
Explanation / Answer
1. Pooling across all possible samples, the distribution of sample means is called the sampling distribution of the sample mean. True or False. Why?
TRUE. It is by definition that this is true. That is how we get the sampling distribution.
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2. The standard error of the sample mean is never larger than the standard deviation of the population distribution. True or False. Why?
TRUE. This is because the standard error is the standard deviation divided by sqrt(n), which is always larger than 1.
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3. The sampling distribution of the sample mean can be approximated by plotting a histogram of the sample data. True or False. Why?
FALSE. The sampling distribution of the mean is approimately normally distirbuted for large enough sample size regardless of the original distribution of data, by central limit theorem.
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4. To study the household income in California, the state government hired two companies. Company A randomly selected 1000 families and reported that the mean income was 74000. Company B randomly selected 2000 families and reported that the mean income was 76000. The government officials should consider company B’s result more reliable. True or False. Why?
TRUE. By the law of large numbers, the larger, the sample size, most probably the sample mean is closer to the population mean.
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