91影视

$\begin{array}{rrr}\text{Sample 1}& \text{Sample 2}& \text{Difference D}\\ 45.9& 35.7& 10.2\\ 41.9& 39.2& 2.7\\ 37.5& 31.1& 6.4\\ 33.4& 28.1& 5.3\\ 31& 24& 7\\ 30.5& 28.7& 1.8\\ 30.9& 25.9& 5\\ 31.9& 23.3& 8.6\\ 30.4& 23.1& 7.3\\ 27.3& 23.7& 3.6\\ 20.4& 20.9& -0.5\\ 24.5& 16.1& 8.4\\ 20.9& 19.9& 1\\ 18.9& 15.2& 3.7\\ 13.7& 11.5& 2.2\\ 11.4& 11.2& 0.2\\ Mean& & 4.5563\\ Sd& & 3.2255\end{array}$

The mean is the sum of all values divided by the number of values:

$$\begin{gathered} \stackrel{炉}{x}=\frac{10.2+2.7+鈥�+2.2+0.2}{16} \\ 鈮�4.5563 \end{gathered}$$

$n$is the number of values in the data set.

The variance is the sum of squared deviations from the mean divided by$n-1$:

localid="1650087093425" $$\begin{gathered} s^2=\frac{(10.2-4.5563{)}^2+鈥�..+(0.2-4.5563{)}^2}{16-1} \\ 鈮�10.4040 \end{gathered}$$

The standard deviation is the square root of the variance:

localid="1650087102851" $$\begin{gathered} s=\sqrt{10.4040} \\ 鈮�3.2255 \end{gathered}$$

Determine the t-value by looking in the row starting with degrees of freedom $n-1=16-1=15$and in the row with $c=95\%$in table B :

$t^{*}=2.131$

The margin of error is then:

localid="1650087135808" $$\begin{gathered} E=t^{*}路\frac{s}{\sqrt{n}} \\ =2.131脳\frac{3.2255}{\sqrt{16}} \\ 鈮�1.7184 \end{gathered}$$

Then the confidence interval becomes:

localid="1650087172012" $$\begin{gathered} 2.8379=4.5563-1.7184 \\ =\stackrel{炉}{x}-E<渭<\stackrel{炉}{x}+E \\ =4.5563+1.7184 \\ =6.2747 \end{gathered}$$

$\begin{array}{rrr}\text{Sample 1}& \text{Sample 2}& \text{Difference D}\\ 45.9& 35.7& 10.2\\ 41.9& 39.2& 2.7\\ 37.5& 31.1& 6.4\\ 33.4& 28.1& 5.3\\ 31& 24& 7\\ 30.5& 28.7& 1.8\\ 30.9& 25.9& 5\\ 31.9& 23.3& 8.6\\ 30.4& 23.1& 7.3\\ 27.3& 23.7& 3.6\\ 20.4& 20.9& -0.5\\ 24.5& 16.1& 8.4\\ 20.9& 19.9& 1\\ 18.9& 15.2& 3.7\\ 13.7& 11.5& 2.2\\ 11.4& 11.2& 0.2\\ Mean& & 4.5563\\ Sd& & 3.2255\end{array}$

Confidence interval found in exercise part (a):

$2.8925<渭<6.2201$

The confidence interval does not contain $0$and thus there is convincing evidence of a difference in the two methods of estimating tire wear.