1. Consider the population shown in the histogram and the sampling distribution

Question

1. Consider the population shown in the histogram and the sampling distribution of the sample mean using a sample size of 30. What is the sample of the population distribution? a. b. What will be the shape of the sampling distribution? Explain how you know c. Compare the mean of the population and the sampling distribution by filling in the blank with ,ors mean of populationmean of sampling distribution d. Compare the standard deviation of the population and the sampling distribution by illing in the blank with , or std dev of populationstd dev of sampling distribution

Explanation / Answer

1.

(a) Sample of Population Distribution is a subset of observations in population .

(b) Shape of Sampling distribution will be Normally distibuted because when we take multiple samples from population and plot their means , the means follow normal distribution. This also follows from Central Limit Theorem .

(c) Mean of Population = Mean of Sampling Distribution

We assume that mean of sampling distribution is an unbiased estimator of population mean.

(d)  Std Dev of population > Std Dev of Sampling Distribution

Sample Means are less variable than the individual values in the population beacuse each sample mean averages together all the values in the sample. A population consists of individual outcomes that can take on a wide range of values. However, if a sample contains an extreme value, although this value will have an effect on the sample mean, the effect is reduced because the value is averaged with all the other values in the sample. As the sample size increases, the effect of a single extreme value becomes smaller because it is averaged with more values.

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2.

There are 3 histograms and sample sizes are 2, 10, 30

Second Histogram's spread > First Histogram's Spread > Third Histogram's spread

The spread is more when sample size is less, as the sample size increases the distribution becomes less spread and approaches noraml distribution. Hence ,

Second Histogram's size (2) < First Histogram's Size (10) < Third Histogram's size(30)

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