Question

3. Find the rejection region (for the standardized test statistic) for each hypothesis test. Identify the test as left-tailed, right-tailed, or two-tailed.

1. H0:μ=141H0:μ=141 vs. Ha:μ<141Ha:μ<141 @ α=0.20.α=0.20.
2. H0:μ=−54H0:μ=−54 vs. Ha:μ<−54Ha:μ<−54 @ α=0.05.α=0.05.
3. H0:μ=98.6H0:μ=98.6 vs. Ha:μ≠98.6Ha:μ≠98.6 @ α=0.05.α=0.05.
4. H0:μ=3.8H0:μ=3.8 vs. Ha:μ>3.8Ha:μ>3.8 @ α=0.001.

Answer 1

1) Rejection region is on the left as the alternate hypothesis is less than type.

The rejection region for standardised test statistic is given by a point on the standard normal curve below which the probability is 0.20.

So the point is -0.84.

2) Rejection region is to the left as the alternate hypothesis is less than type.

The rejection region for standardised test statistic is given by a point on the standard normal curve below which the probability is 0.05.

So the point is -1.64.

3) Rejection region is on the both sides of the normal distribution graph as the alternate hypothesis is not equal to type.

The rejection region for standardised test statistic is given by a point on the standard normal curve below which the probability is 0.025 as the 0.05 probability is divided on both sides.

So the point is -1.96.

4) Rejection region is to the right as the alternate hypothesis is greater than type.

The rejection region for standardised test statistic is given by a point on the standard normal curve above which the probability is 0.001.

So the point is 3.09.

Thank you !!!