(a)A random sample of 10 children (9 years old) showed that they had an average REM (rapid eye movement) sleep time of 3.8 hours per night. From previous studies it is known that the standard deviation of 0.4 hour. Another random sample of 15 adults showed that they and an average REM sleep time of 3.1 hours per night. Previous studies show that the standard deviation was 0.8 hour. Is there enough evidence to support the conclusion that children get more REM sleep than adults? Use a 5% level of significance.      At the 5% level of significance there is sufficient evidence to reject the null hypothesis and we conclude that children get more REM sleep than adults.       At the 5% level of significance there is insufficient evidence to reject the null hypothesis and we conclude that children get more REM sleep than adults.       At the 5% level of significance there is sufficient evidence to reject the null hypothesis and we conclude that children do not get more REM sleep than adults.       At the 5% level of significance there is insufficient evidence to reject the null hypothesis and we conclude that children do not get more REM sleep than adults.   (b)When you read a statement, “From previous knowledge, it is known that the standard deviation is 4.28 for group 1 and 5.6 for group 2,” you would

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(a)A random sample of 10 children (9 years old) showed that they had an average REM (rapid eye movement) sleep time of 3.8 hours per night. From previous studies it is known that the standard deviation of 0.4 hour. Another random sample of 15 adults showed that they and an average REM sleep time of 3.1 hours per night. Previous studies show that the standard deviation was 0.8 hour. Is there enough evidence to support the conclusion that children get more REM sleep than adults? Use a 5% level of significance. 
 
 
At the 5% level of significance there is sufficient evidence to reject the null hypothesis and we conclude that children get more REM sleep than adults.
 
 
 
At the 5% level of significance there is insufficient evidence to reject the null hypothesis and we conclude that children get more REM sleep than adults.
 
 
 
At the 5% level of significance there is sufficient evidence to reject the null hypothesis and we conclude that children do not get more REM sleep than adults.
 
 
 
At the 5% level of significance there is insufficient evidence to reject the null hypothesis and we conclude that children do not get more REM sleep than adults.
 
(b)When you read a statement, “From previous knowledge, it is known that the standard deviation is 4.28 for group 1 and 5.6 for group 2,” you would run which test: 
 
 
 
T-Test
 
 
 
Z-Test
 
 
 
2-Samp Z Test
 
 
 
2-Samp T Test
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