Question

consider the following hypothesis test, H0, U greater than or equal to 20, Ha less than 20, a sample of 50, provided a mean of 19.4 population standard deviation is 2, compute the value of of the test static, what is the p-value,

Answer 1

Based on the calculations, the value of the test statistic and p-value are equal to -2.1213 and 0.0169 respectively.

Given the following data:

• Standard deviation = 2.

• Sample mean = 19.4.

• Number of sample = 50.

• Hypothesized mean = 20.

How to compute the test static?

Mathematically, the value of the test statistic can be computed by using this formula:

$Z=\frac{\bar{x}\;-\;\mu}{ \frac{\sigma}{\sqrt{n} } }\\\\Z=\frac{19.4\;-\;20}{\frac{2}{\sqrt{50}}}\\\\Z=\frac{-0.6}{0.282842 }$

zₓ = -2.1213.

From the z-table, the p-value is given by:

P(Z < zₓ) = P(Z < -2.1213)

P(Z < -2.1213) = 0.0169.

Since the p-value is equal to 0.0169 less than α = 0.05, we would reject H₀ : µ equal to 20. Thus, we would conclude that µ < 20.

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