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 n1 = 11 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that ?1 = 0.6 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.2 hours per night. Previous studies show that ?2 = 0.7 hour.(a) 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 x₂ = 2.9 hours per night. From previous studies, it is known that a, 0.6 hour. Another random sample of n₂ = 11 adults.showed that they had an average REM sleep time of x₂ = 2.2 hours per night. Previous studies show that ₂ -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.H₂i Hqi Hy H₂Ho: M₁ⒸH₂ H₁ H₂i H₂= H₂ (iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significantO 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.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 statistically significant.level a?(v) Interpret your conclusion in the context of the application.O Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults.O 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.O 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 #₁ #₂. (Round your answers to two decimal places.)lower limitupper limitExplain the meaning of the confidence interval in the context of the problem.O Because the interval contains only positive numbers, this indicates that at the 98% confidence level, the population mean REM sleep time for children is greater than that for adults.O Because the interval contains both positive and negative numbers, this indicates that at the 98% confidence level, we can not say that the population mean REM sleep time for children is greater than that for adults.O We can not make any conclusions using this confidence interval.O Because the interval contains only negative numbers, this indicates that at the 98% confidence level, the population mean REM sleep time for children is less than that for adults.

Question

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 n1 = 11 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that ?1 = 0.6 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.2 hours per night. Previous studies show that ?2 = 0.7 hour.(a) 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 x₂ = 2.9 hours per night. From previous studies, it is known that a, 0.6 hour. Another random sample of n₂ = 11 adults.showed that they had an average REM sleep time of x₂ = 2.2 hours per night. Previous studies show that ₂ -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.H₂i Hqi Hy > H₂Ho: M₁ⒸH₂ H₁ H₂i H₂= H₂ (iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significantO 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.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 statistically significant.level a?(v) Interpret your conclusion in the context of the application.O Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults.O 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.O 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 #₁ #₂. (Round your answers to two decimal places.)lower limitupper limitExplain the meaning of the confidence interval in the context of the problem.O Because the interval contains only positive numbers, this indicates that at the 98% confidence level, the population mean REM sleep time for children is greater than that for adults.O Because the interval contains both positive and negative numbers, this indicates that at the 98% confidence level, we can not say that the population mean REM sleep time for children is greater than that for adults.O We can not make any conclusions using this confidence interval.O Because the interval contains only negative numbers, this indicates that at the 98% confidence level, the population mean REM sleep time for children is less than that for adults.

Accepted Answer

Given :
n1=11x¯1=2.9σ1=0.6n2=11x¯2=2.2σ2=0.7
level of significance is 1%