Question

Please give step by step explanations.  

A statistician randomly sampled n observations from a normal distribution with population standard deviation of 17, and found x = 103. Assume that the null and alternative hypothesis are given by

H0 :  μ= 110 v.s. Ha : μ < 110

Give the range of all possible values of n for which the statistician will reject the null hypothesis at the significance level α = 0.1003.

Question 50 options:

	n ≥7
	n ≥ 8
	n ≥ 9
	n ≥ 10

Answer 1

Answer: n ≥ 10

Explanation:

1)

if we take n= 7 then,

= 17,  = 110

= 103

= 0. 0.1003

null and alternative hypothesis is

Ho:   = 110

H1:   < 110

formula for test statistics is

z = -1.09

test statistics Z = -1.09

calculate P-Value

P-Value = P(z < -1.09)

using normal z table we get

P(z < -1.09) = 0.1380

P-Value = 0.1380

Decision rule is

Reject Ho if ( P-Value) ( )

here, ( P-Value = 0.1380) > ( = 0.1003)

Hence,

Null hypothesis is NOT rejected.

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2)

if n= 8

test statistics Z = -1.16

P-Value = 0.1221

Decision rule is

Reject Ho if ( P-Value) ( )

here, ( P-Value = 0.1221) > ( = 0.1003)

Hence,

Null hypothesis is NOT rejected.

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3)

if n= 9

test statistics Z = -1.24

P-Value = 0.1084

Decision rule is

Reject Ho if ( P-Value) ( )

here, ( P-Value = 0.1084) > ( = 0.1003)

Hence,

Null hypothesis is NOT rejected.

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4)

if n= 10

test statistics Z = -1.30

P-Value = 0.0964

Decision rule is

Reject Ho if ( P-Value) ( )

here, ( P-Value = 0.0964) < ( = 0.1003)

Hence,

Null hypothesis is rejected.

Thus we find that Null Hypothesis is rejected if  n ≥ 10