Consider the following three relative frequency histograms. Each histogram was constructed by selecting 100 random samples from a population composed of 40% women and 60% men. For each sample, the sample proportion of women, p̂, was calculated and the 100 p̂ values were used to construct the histogram. For each histogram, a different sample size was used. One histogram was constructed using 100 samples of size 20, one was constructed using 100 samples of size 40, and one was constructed using 100 samples of size 100.Histogram IThe histogram has 6 rectangles. The horizontal axis is labeled "Sample proportion." The vertical axis is labeled "Relative frequency." The approximate points on the horizontal axis that the rectangles are centered at and the heights of the rectangles are as follows:0.25: 0.01 unit tall0.3: 0.07 unit tall0.35: 0.24 unit tall0.4: 0.42 unit tall0.45: 0.22 unit tall0.5: 0.04 unit tall Histogram IIThe histogram has 11 rectangles. The horizontal axis is labeled "Sample proportion." The vertical axis is labeled "Relative frequency." The approximate points on the horizontal axis that the rectangles are centered at and the heights of the rectangles are as follows:0.15: 0.01 unit tall0.2: 0.02 unit tall0.25: 0.06 unit tall0.3: 0.13 unit tall0.35: 0.17 unit tall0.4: 0.18 unit tall0.45: 0.17 unit tall0.5: 0.13 unit tall0.55: 0.08 unit tall0.6: 0.04 unit tall0.65: 0.01 unit tall Histogram IIIThe histogram has 9 rectangles. The horizontal axis is labeled "Sample proportion." The vertical axis is labeled "Relative frequency." The approximate points on the horizontal axis that the rectangles are centered at and the heights of the rectangles are as follows:0.25: 0.02 unit tall0.3: 0.09 unit tall0.35: 0.27 unit tall0.4: 0.22 unit tall0.45: 0.21 unit tall0.5: 0.11 unit tall0.55: 0.06 unit tall0.6: 0.01 unit tall0.65: 0.01 unit tall(a)These three histograms are approximate sampling distributions of p̂ for the three different sample sizes. Which histogram corresponds to the sample size that would produce sample proportions that varied the most from sample to sample?Histogram IHistogram II Histogram III(b)Match the three sample sizes to the three histograms. That is, which histogram is the approximate sampling distribution for sample size = 20, which is for sample size = 40, and which is for sample size = 100?Histogram In= ---Select--- 20 40 100Histogram IIn= ---Select--- 20 40 100Histogram IIIn= ---Select--- 20 40 100Explain how you made your choices.Sample-to-sample variability ---Select--- increases stays the same decreases as the sample size increases.

Question

Consider the following three relative frequency histograms. Each histogram was constructed by selecting 100 random samples from a population composed of 40% women and 60% men. For each sample, the sample proportion of women, p̂, was calculated and the 100 p̂ values were used to construct the histogram. For each histogram, a different sample size was used. One histogram was constructed using 100 samples of size 20, one was constructed using 100 samples of size 40, and one was constructed using 100 samples of size 100.Histogram IThe histogram has 6 rectangles. The horizontal axis is labeled &#34;Sample proportion.&#34; The vertical axis is labeled &#34;Relative frequency.&#34; The approximate points on the horizontal axis that the rectangles are centered at and the heights of the rectangles are as follows:0.25: 0.01 unit tall0.3: 0.07 unit tall0.35: 0.24 unit tall0.4: 0.42 unit tall0.45: 0.22 unit tall0.5: 0.04 unit tall Histogram IIThe histogram has 11 rectangles. The horizontal axis is labeled &#34;Sample proportion.&#34; The vertical axis is labeled &#34;Relative frequency.&#34; The approximate points on the horizontal axis that the rectangles are centered at and the heights of the rectangles are as follows:0.15: 0.01 unit tall0.2: 0.02 unit tall0.25: 0.06 unit tall0.3: 0.13 unit tall0.35: 0.17 unit tall0.4: 0.18 unit tall0.45: 0.17 unit tall0.5: 0.13 unit tall0.55: 0.08 unit tall0.6: 0.04 unit tall0.65: 0.01 unit tall Histogram IIIThe histogram has 9 rectangles. The horizontal axis is labeled &#34;Sample proportion.&#34; The vertical axis is labeled &#34;Relative frequency.&#34; The approximate points on the horizontal axis that the rectangles are centered at and the heights of the rectangles are as follows:0.25: 0.02 unit tall0.3: 0.09 unit tall0.35: 0.27 unit tall0.4: 0.22 unit tall0.45: 0.21 unit tall0.5: 0.11 unit tall0.55: 0.06 unit tall0.6: 0.01 unit tall0.65: 0.01 unit tall(a)These three histograms are approximate sampling distributions of p̂ for the three different sample sizes. Which histogram corresponds to the sample size that would produce sample proportions that varied the most from sample to sample?Histogram IHistogram II    Histogram III(b)Match the three sample sizes to the three histograms. That is, which histogram is the approximate sampling distribution for sample size = 20, which is for sample size = 40, and which is for sample size = 100?Histogram In= ---Select--- 20 40 100Histogram IIn= ---Select--- 20 40 100Histogram IIIn= ---Select--- 20 40 100Explain how you made your choices.Sample-to-sample variability  ---Select--- increases stays the same decreases as the sample size increases.

Accepted Answer

Given that,
Three histograms,