Question

Consider the following hypothesis test:H0: 20Ha: < 20A sample of 60 provided a sample mean of 19.6. The population standard deviation is 1.6.A sample of 60 provided a sample mean of 19.6. The population standard deviation is 1.6.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)?d. Using = .05, what is the critical value for the test statistic (to 3 decimals)? If your answer is negative, use minus "-" sign. _______What is the rejection rule using the critical value?Reject H0 if z ____ _____

Answer 1

Answer:

a: z = -1.936

b: 0.0265

d: z < -1.645

Reject H0 if z < -1.645

Step-by-step explanation:

We are given:

H0:  µ = 20

HA:  µ < 20

n = 60, sample mean: 19.6, σ = 1.6

Since the alternate hypothesis has a < sign in it, it is a left tailed test.  The < or > sign in the alternate hypothesis points towards the rejection region.

For a:  We need to calculate the test statistic for our situation.  This is done with a z-score formula for samples.  

For b:  we need to use the z-score table to look up the p-value for the score we calculate in part a.  The p-value is 0.0265.  This means that there is only about a 2.65% chance that the sample values were a result of random chance.

For d:  Since the significance level is 0.05, and this is a one tailed test, we have a critical value of z < - 1.645.  This means that if the z-score we calculate in part a is less than -1.645, we will reject the null hypothesis

See attached photo for all the calculations!