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Statistics LibreTexts

8.12: Chapter Solution (Practice + Homework)

  • Page ID
    6079
  • This is a normal distribution curve. The peak of the curve coincides with the point 1.5 on the horizontal axis.  A central region is shaded between points 1.38 and 1.62.

    Figure \(\PageIndex{23}\)

  • The error bound and confidence interval will decrease.
  • 136.

    1. \(\overline x = $568,873\)
    2. \(CL = 0.95\) \(\alpha = 1 – 0.95 = 0.05\) \(z_{\frac{\alpha}{2}}=1.96\)
      \(E B M=z_{0.025} \frac{\sigma}{\sqrt{n}}=1.96 \frac{909200}{\sqrt{40}}=\$ 281,764\)
    3. \(\overline x − EBM = 568,873 − 281,764 = 287,109\)
      \(\overline x + EBM = 568,873 + 281,764 = 850,637\)
    4. We estimate with 95% confidence that the mean amount of contributions received from all individuals by House candidates is between $287,109 and $850,637.

    139.

    Higher

    140.

    It would increase to four times the prior value.

    141.

    No, It could have no affect if it were to change to \(1 – p\), for example. If it gets closer to 0.5 the minimum sample size would increase.

    142.

    Yes

    143.

    1. No
    2. No