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Consider the following hypothesis test: H 0: 20 H a: < 20 A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2. a. Compute the value of the test statistic (to 2 decimals). If your answer is negative, use minus "-" sign b. What is the p-value (to 3 decimals)

Respuesta :

Answer: p-value is 0.016.

Step-by-step explanation:

Since we have given that

[tex]H_0:\mu=20\\\\H_a:\mu<20[/tex]

Sample mean = 19.4

Sample size n = 50

Standard deviation = 2

We need to find the test statistic value which is given by

[tex]z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\\\z=\dfrac{19.4-20}{\dfrac{2}{\sqrt{50}}}\\\\\\z=\dfrac{-0.6}{0.28}\\\\z=-2.14[/tex]

p-value is given by

[tex]P(Z>Z_{critical})\\\\=P(Z>-2.14)\\\\=0.016[/tex]

Hence, p-value is 0.016.

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