Please see attached mathematical statistics question below.part(c)How to determine Compute the p-value and briefly write your conclusion? The life of a tire in miles, say X, is normally distributed with mean e and standard deviation 4 (inthousands). Past experience indicates that 0 = 25 (in thousands). The manufacturer claims that thetires made by a new process have mean 0 > 25 (in thousands). Check his claim by testing Ho : 0 = 25(in thousands) versus H1 : 0 > 25 (in thousands). We observed n independent values of X, sayT1,..., In and we reject Ho if and only if i 2 c.(a) Identify the test statistics and the critical region. Express e in terms of the significance level a.(b) Determine n and e so that the power function y(8) of the test has the values y(25) = 0.04 and(28) = 0.96.(c) Suppose we observed a sample of size 64 with a sample mean i = 26 (in thousands). Computethe p-value and briefly write your conclusion.

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Description: Please see attached mathematical statistics question below.part(c)How to determine Compute the p-value and briefly write your conclusion? The life of a tire in miles, say X, is normally distributed with mean e and standard deviation 4 (inthousands).

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Please see attached mathematical statistics question below.

part(c)

How to determine Compute the p-value and briefly write your conclusion?

The life of a tire in miles, say X, is normally distributed with mean e and standard deviation 4 (in
thousands). Past experience indicates that 0 = 25 (in thousands). The manufacturer claims that the
tires made by a new process have mean 0 > 25 (in thousands). Check his claim by testing Ho : 0 = 25
(in thousands) versus H1 : 0 > 25 (in thousands). We observed n independent values of X, say
T1,..., In and we reject Ho if and only if i 2 c.
(a) Identify the test statistics and the critical region. Express e in terms of the significance level a.
(b) Determine n and e so that the power function y(8) of the test has the values y(25) = 0.04 and
(28) = 0.96.
(c) Suppose we observed a sample of size 64 with a sample mean i = 26 (in thousands). Compute
the p-value and briefly write your conclusion.

Expert Solution

Step 1

Given information-

Population mean, θ = 25

Population standard deviation, σ = 4

Sample size, n = 64

Sample mean, x-bar = 26

Given hypothesis-

Null Hypothesis, H₀: θ = 25

Alternate Hypothesis, H_a: θ > 25

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