Q4. Sample surveys conducted in a large country in a certain year and again 20 years later showed that originally the average height of 420 ten-year-old boys was 54 inches with a sam- ple standard deviation of 2.8 inches. On the other hand, 20 years later, the average height of 480 ten-year-old boys was 56 inches with a sample standard deviation of 2.4 inches. Test the hypothesis Ho : 1 - 12 = -0.5 against the alternative H : m-2< -0.5 at 0.05 level of significance where H and 2 are the true average heights of boys 20 years before and after, respectively. Suppose the populations are normally distributed. (i). Test the hypothesis by finding the Critical Region. (ii). Test the hypothesis by finding the P-value (note that you do not need to find the exact P-value from the table. But, you can still conduct the test).

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Plzz solve i) and ii) and explain
Q4.
Sample surveys conducted in a large country in a certain year and again 20 years later
showed that originally the average height of 420 ten-year-old boys was 54 inches with a sam-
ple standard deviation of 2.8 inches. On the other hand, 20 years later, the average height of
480 ten-year-old boys was 56 inches with a sample standard deviation of 2.4 inches. Test the
hypothesis Ho : 41 – 42 = -0.5 against the alternative H1 : 41 - 42 < -0.5 at 0.05 level of
significance where 41 and 2 are the true average heights of boys 20 years before and after,
respectively. Suppose the populations are normally distributed.
(i). Test the hypothesis by finding the Critical Region.
(ii). Test the hypothesis by finding the P-value (note that you do not need to find the
exact P-value from the table. But, you can still conduct the test).
Transcribed Image Text:Q4. Sample surveys conducted in a large country in a certain year and again 20 years later showed that originally the average height of 420 ten-year-old boys was 54 inches with a sam- ple standard deviation of 2.8 inches. On the other hand, 20 years later, the average height of 480 ten-year-old boys was 56 inches with a sample standard deviation of 2.4 inches. Test the hypothesis Ho : 41 – 42 = -0.5 against the alternative H1 : 41 - 42 < -0.5 at 0.05 level of significance where 41 and 2 are the true average heights of boys 20 years before and after, respectively. Suppose the populations are normally distributed. (i). Test the hypothesis by finding the Critical Region. (ii). Test the hypothesis by finding the P-value (note that you do not need to find the exact P-value from the table. But, you can still conduct the test).
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