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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 n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that ?1 = 0.6 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that ?2 = 0.5 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 10% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.) test statistic critical value…5 The probability of success in each trial is equal to 0.25 . Using the Chebyshev-Bienaymè inequality, estimate the probability that in 800 independent trials the number of successes will be greater than 150 , but less than 250 .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 = 9 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 σ1 = 0.5 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.20 hours per night. Previous studies show that σ2 = 0.7 hour. (a) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ1 − μ2. Round your answer to two decimal places.)(b) Find (or estimate) the P-value. (Round your answer to four decimal places.) (c) Find a 98% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit
- 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 = 2.5 hours per night. From previous studies, it is known that σ1 = 0.7 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.00 hours per night. Previous studies show that σ2 = 0.6 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 10% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference μ1 − μ2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.) test statistic critical value…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 = 9 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 σ1 = 0.6 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that σ2 = 0.8 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (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 n1 = 8 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 = 0.9 hour. Another random sample of n2 = 8 adults showed that they had an average REM sleep time of x2 = 2.00 hours per night. Previous studies show that ?2 = 0.6 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. (a) What is the level of significance?State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 = ?2; H1: ?1 < ?2 H0: ?1 = ?2; H1: ?1 > ?2H0: ?1 < ?2; H1: ?1 = ?2 (b) What sampling distribution will you use? What assumptions are you…
- 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 = 2.20 hours per night. Previous studies show that ?2 = 0.7 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 < ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 > ?2 H0: ?1 = ?2; H1: ?1 < ?2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume…Mention 3 examples of discrete random variables and 3 examples of continuous random variables applied in engineering.If X is a continuous random variable, what is the value of X that will be exceeded 30% of the time, if X has a gamma distribution with a mean of 2 and a variance of 2? (just set up the equation in itssimplest form)
- 7REM (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 = 8 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that ?1 = 0.9 hour. Another random sample of n2 = 8 adults showed that they had an average REM sleep time of x2 = 1.60 hours per night. Previous studies show that ?2 = 0.6 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. what is the sample test statistic find or estimate p valueFor each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish