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Chapter 10: Q. 10.92 (page 429)

Wing Length. Refer to Exercise 10.86 and find a 999 con fidence interval for the difference between the mean wing lengths o the two subspecies.

Short Answer

Expert verified

The interval is -4.488 to -1.111

Step by step solution

01

Given Information.

We have to consider the given table to find the answer :

02

Step 2:Explanation

For a confidence interval of $99 %$

$df = \frac{{[(\frac{s_{1}^{2}}{n_{1}}) + (\frac{s_{2}^{2}}{n_{2}})]}^{2}}{\frac{{(\frac{s_{1}^{2}}{n_{1}})}^{2}}{{(\frac{x_{2}^{2}}{n_{2}})}^{2}}}$

$= \frac{[{(\frac{1 . 501^{2}}{14})}^{2} + {(\frac{1 . 698^{2}}{14})}^{2}}{\frac{{(\frac{1 . 501^{2}}{14})}^{2}}{14 - 1} + \frac{{(\frac{1 . 698^{2}}{14})}^{2}}{14 - 1}}$

$= 25$

The interval's end point is:

$({\bar{x}}_{1} - {\bar{x}}_{2}) \pm t \frac{a}{2} \cdot \sqrt{(\frac{s_{1}^{2}}{n_{1}}) + (\frac{s_{2}^{2}}{n_{2}})}$ $= (82.1 - 84.9) \pm 2.787$ $\sqrt{(\frac{1 . 501^{2}}{14} + \frac{1 . 698^{2}}{14})}$

$= - 4.488 t o - 1.111$

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Most popular questions from this chapter

Refer to Exercise $10.85$ and determine a $98 %$ confidence interval for the difference between the mean dopamine activities of psychotic and nonpsychotic patients.

In each of Exercises 10.35-10.38, we have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case, whether use of the pooled $t$ -test and pooled $t$ -interval procedure is reasonable. Explain your answer.

10.38 $x_{1} = 39.04, s_{1} = 18.82, n_{1} = 51$

$x_{2} = 49.92, s_{2} = 18.97, n_{2} = 53$

O. Ehimwenma and M. Tagbo, researchers in Nigeria, were interested in how the characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. They published their findings in the article "Determination of Normal Dimensions of the Spleen by Ultrasound in an Endemic Tropical Environment" (Nigerian Medical Journal, Vol. 52, No. 3, pp. 198-203). The researchers randomly sampled $91$ males and $109$ females in Nigeria. The mean and standard deviation of the spleen lengths for the males were $11.1 cm$ and $0.9 cm$ respectively, and those for the females were $10.1 cm$ and $0.7 cm$ , respectively. At the $1 %$ significance level, do the data provide sufficient evidence to conclude that a difference exists in mean spleen lengths of male and female Nigerians?

The primary concern is deciding whether the mean of Population 1 is greater than the mean of Population 2

What constitutes each pair in a paired sample?

See all solutions

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