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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…In a survey of 164 publicly-traded companies, the average price-earnings ratio was 18.5 with a standard deviation of 8.9. When testing the hypothesis (at the 5% level of significance) that the average energy use has decreased from the past value of 16.3, what is the critical value? (please round your answer to 2 decimal places)Standing eye heights of women normally distributed with a mean of 1516 mm and a standard deviation of 63 mm. What % of women have a standing eye height between 1420 mm and 1560 mm, and what is the probability that a group of 20 women has an average standing eye height that is less than 1500 mm? Even though the sample size is less than 30, why can the Central Limit Theorem still be applied?
- Please show the bell curve illustrations and please show ever step. Please do not skip a step so I can fully understand step-by-step how to solve the problem. Thank 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 = 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.)What is the absolute difference in the probbility of being less 4 in a triangular distribution with a minimum of 1 and a maximum of 11 and a most likely value of 8 and a beta distribution with the same minimum and maximum and an alpha = beta= 4?
- It has been determined experimentally that steel wires of a certain length have strength with a mean value of 1 kip and a coefficient of variation of 16%. What is the probability that the strength of such a wire is less than 0.7 kips? Try Type I and Type III asymptotic distributions of extremes and compare the results.A random variable x follows Poisson distribution with average 7, Find p(x=4) = Round to 4 decimalsplease help me solve both parts a and b. please do not round your answers. if you solve correctly i will be glad to rate you. thank you so much for your help.
- 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 = 2.5 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 valueQ4 For the tornado events in a certain region, the tornado-induced wind speed can be modeled by a lognormal random variable with a mean value of ux = 120 mph and a standard deviation of ox = 12 mph. a) Calculate the probability that the wind speed will be between 100 mph and 130 mph in a tornado event. b) If a structure located in this region is designed to resist for wind speed of 150 mph, what is the probability that the structure will be damaged during such a tornado?The lifespan of a 100-W fluorescent lamp is define to be normally distributed with σ = 30 hrs. A random sample of 15 lamps has a mean life of x = 1000 hours. Construct a 90% lower-confidence bound on the mean life.