Question

Hallo B I U a. Av obca v ili u A1 fx Amount B C D E F G 1 اهم الا Amount 2 20.50 3 14.63 23.77 29.96 6 29.49 7 32.70 8 9.20 9 20.89 10 28.87 11 15.78 12 18.16 13 12.16 14 11.22 15 16.43 16 17.66 17 9.59 18 18.89 19 19.88 20 23.11 21 20.11 22 20.34 23 20.08 24 30.36 25 21.79 26 21.18 27 19.22 28 34.13 29 27.49 30 36.55 31 18.37 32 32.27 33 12.63

Answer 1

Given :

$n = 64 , \sigma = 13$

20.5	18.16	20.34	32.27	13.63	6.83	26.46
14.63	12.16	20.08	12.63	17.22	30.99	24.24
23.77	11.22	30.36	25.53	13.17	14.62	16.66
29.96	16.43	21.79	27.71	20.12	18.38	20.85
29.49	17.66	21.18	33.81	22.11	26.85
32.7	9.59	19.22	21.79	22.47	25.1
9.2	18.89	34.13	19.16	20.36	27.55
20.89	19.88	27.49	26.35	35.47	25.87
28.87	23.11	36.55	20.01	11.85	14.37
15.78	20.11	18.37	26.85	17.88	15.61

From the given values, the sample mean calculated is

$\bar{x} = 21.52$

$\alpha = 0.01, \alpha /2 = 0.005$

Hece the critical value of z will be,

-a/2 70.005 = 2.58

Solution :

a)

At 99% confidence, the margin of error (E) is

$E = z_{0.005}\frac{\sigma }{\sqrt{n}}$

$E = 2.58\frac{13 }{\sqrt{64}} = 4.19$

At 99% confidence, the margin of error is $4.19.

b)

99% confidence interval can be calculated as

$\bar{x} \pm z_{0.005}\frac{\sigma }{\sqrt{n}}$

$21.52 \pm 4.19$

99% confidence interval estimate of the mean amount spent for lunch is $17.33 to $25.71.

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