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REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 11 children (9 years old) showed that they had an average REM sleep time of , = 2.9 hours per night. From previous studies, it is known that a, - 0.6 hour. Another random sample of n, = 11 adults showed that they had an average REM sleep time of x, = 2.2 hours per night. Previous studies show that o, = 0.7 hour. (a) Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. 1) what is the level of significance? State the null and alternate hypotheses. (1H) what sampling distribution will you use? What assumptions are you making? The Student's . We assume that both population distributions are approximacely normal with known standard deviations. The Student's t. We assume that both population distributions are approscimately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. • The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? Compute the corresponding z or rvalue as appropriate. (Test the difference , -Hy. Round your answer to two decimal places.) (ii) Find (or estimate) the Prvalue. (Round your answer to four decimal places.)

REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 11 children (9 years old) showed that they had an average REM sleep time of , = 2.9 hours per night. From previous studies, it is known that a, - 0.6 hour. Another random sample of n, = 11 adults showed that they had an average REM sleep time of x, = 2.2 hours per night. Previous studies show that o, = 0.7 hour. (a) Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. 1) what is the level of significance? State the null and alternate hypotheses. (1H) what sampling distribution will you use? What assumptions are you making? The Student's . We assume that both population distributions are approximacely normal with known standard deviations. The Student's t. We assume that both population distributions are approscimately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. • The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? Compute the corresponding z or rvalue as appropriate. (Test the difference , -Hy. Round your answer to two decimal places.) (ii) Find (or estimate) the Prvalue. (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(iv) Based on your answers in parts (i)-(i), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. P Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. Reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults. Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults. O Fail to reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. (b) Find a 98% confidence interval for u, - H,. (Round your ansvers to two decimal places.) lower limit upper limit
Transcribed Image Text:(iv) Based on your answers in parts (i)-(i), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. P Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. Reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults. Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults. O Fail to reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. (b) Find a 98% confidence interval for u, - H,. (Round your ansvers to two decimal places.) lower limit upper limit
REM (rapid eye movement) sleep is sleep during which most dreams ocur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults.t Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 11 children (9 years old) showed that they had an average REM sleep time of x, = 2.9 hours per night. From previous studies, it is known that o, = 0.6 hour. Another random sample of n, = 11 adults showed that they had an average REM sleep time of x, = 2.2 hours per night. Previous studies show that o, = 0.7 hour. (a) Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (i) What is the level of significance? State the null and alternate hypotheses. (ii) what sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O P The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? Compute the corresponding z or t-value as appropriate. (Test the difference u, - H. Round your answer to two decimal places.) (iii) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Transcribed Image Text:REM (rapid eye movement) sleep is sleep during which most dreams ocur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults.t Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 11 children (9 years old) showed that they had an average REM sleep time of x, = 2.9 hours per night. From previous studies, it is known that o, = 0.6 hour. Another random sample of n, = 11 adults showed that they had an average REM sleep time of x, = 2.2 hours per night. Previous studies show that o, = 0.7 hour. (a) Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (i) What is the level of significance? State the null and alternate hypotheses. (ii) what sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O P The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? Compute the corresponding z or t-value as appropriate. (Test the difference u, - H. Round your answer to two decimal places.) (iii) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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