Question

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)

Answer 1

Answer: p-value is 0.016.

Explanation:

Since we have given that

`H_0:\mu=20\\\\H_a:\mu<20`

Sample mean = 19.4

Sample size n = 50

Standard deviation = 2

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

`z=\frac{\bar{x}-\mu}{(\sigma)/(√(n))}\\\\\\z=(19.4-20)/((2)/(√(50)))\\\\\\z=(-0.6)/(0.28)\\\\z=-2.14`

p-value is given by

`P(Z>Z_(critical))\\\\=P(Z>-2.14)\\\\=0.016`

Hence, p-value is 0.016.