Question

Q111/11C Q2 (0.5/1) Q3 [1/1]CQ4(0.8/1) Q 15 11/1] Grade: 13.3/15 Print Version You measure 20 backpacks' weights, and find they have a mean weight of 57 ounces. Assume the population standard deviation is 9.4 ounces. Based on this, construct a 90% confidence interval for the true population mean backpack weight. Give your answers as decimals, to two places 57 3.65 ounces

Answer 1

1.

At $\small \alpha$ = 0.10, the critical value, z_c = 1.645

90% confidence interval for the tre population mean

$\small \bar x \pm z_c*\frac{\sigma}{\sqrt{n}}$

$\small 57 \pm 1.645*\frac{9.4}{\sqrt{20}}$

$\small \textbf{57} \pm \textbf{3.46}$

2. $\small \small n= 10, \ \bar x = 41, \ s = 2$

At $\small \alpha$ = 0.20 and df = 10-1=9, the critical value, t_c = 1.383

Margin of error, E =

$\small E= t_c*\frac{s}{\sqrt{n}} = 1.383*\frac{2}{\sqrt{10}} =\textbf{0.87}$

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