Question

In: Statistics and Probability

Consider the following computer output: Test of mu = 91 vs > 91 Variable N Mean...

Consider the following computer output:

Test of mu = 91 vs > 91

Variable	N	Mean	StDev	SE Mean
x	20	92.44	0.717	0.16

Find the 95% Lower bound.

Expert Solution

SOLUTION:

From given data,

Null and Alternative hypothesis:

H₀ = 91 vs H_a > 91

Find the 95% Lower bound.

Where,

sample = N = 20

sample mean = = 92.44

standard deviation = =0.717

Confidence interval is 95%

95% = 95/100 = 0.95

= 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

Z_/2 = Z_0.025 = 1.96

The Lower bound is

Lower bound = - Z_/2 * ( / )

= 92.44 - 1.96 * (0.717 / √20 )

= 92.44 - 1.96 * (0.717 / 4.4721359)

= 92.44 - 1.96 * 0.160326

= 92.44 - 0.31423896

= 92.1257

The 95% Lower bound is 92.1257

orchestra answered 2 years ago

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