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 adultst. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 8 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 ơ, = 0.6 hour. Another random sample of n, = 8 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that o, = 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. (a) What is the level of significance? State the null and alternate hypotheses. O Hoi H1 = Hz; HHy> H2 O Hoi Hy

The yield in pounds from a day's production is normally distributed with a mean of 1500 pounds and standard deviation of 100 pounds. Assume that the yields on different days are independent random variables. What is the probability that the production yield exceeds 1400 pounds on at least four of the five days next week?

Suppose we have a normal distribution N(2, 4), using the Empirical rule, what proportion of data is between the data values -2 and 6?

The amounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of 24minutes and a standard deviation of 5 minutes. Find the probability that a randomly selected athlete uses a stair climber for​   (a) less than 21 ​minutes, (b) between 24 and 32 minutes (c) more than 40 minutes. ​

Donating Blood to Grandma?Can young blood help old brains? Several studies1 in mice indicate that it might. In the studies, old mice (equivalent to about a 70-year-old person) were randomly assigned to receive blood plasma either from a young mouse (equivalent to about a 25-year-old person) or another old mouse. The mice receiving the young blood showed multiple signs of a reversal of brain aging. One of the studies2 measured exercise endurance using maximum treadmill runtime in a 90-minute window. The number of minutes of runtime are given in the table below for the 17 mice receiving plasma from young mice and the 13 mice receiving plasma from old mice. The data are also available in YoungBlood. Young 27 28 31 35 39 40 45 46 55 56 59 68 76 90 90 90 90         Old 19 21 22 25 28 29 29 31 36 42 50 51 68   Round your answers to two decimal places.(a) Calculate , the mean number of minutes on the treadmill for those mice receiving young blood.Enter your answer in…

Data originally from DASL http://lib.stat.cmu.edu/DASL/Datafiles/CancerSurvival.html (Links to an external site.). Some bronchial cancer patients had the following survival times (in days) after receiving a certain treatment: 20, 37, 63, 64, 72, 81, 138, 151, 155, 166, 166, 223, 245, 246, 450, 459.  (The second instance of “166” is not a mistake.) Do these numbers suggest that the average survival time, for all bronchial cancer patients who receive that treatment, is significantly different from 200 days? CANCER SURVIVAL Report an appropriate one-sample hypothesis test and use a 10% significance level. For Step 4 of the six-step process that was taught in this class, choose the BEST option to complete the following sentence: We assume that the sample of subjects is a SRS and we assume that the population of observations has no outliers ... and is Normally distributed. and is without a doubt bell-shaped. and is Uniformly distributed. (nothing needs to go here because the sample…

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in thedusLove uo useful life (150,000 miles of driving) of cars of a particular model varies Normall/ih nean 80 mg/mi and standard deviation 4 mg/mi. A company has 25 cars of this model in its et find the level L such that the probability that the average NOX+NMOG level 7 for the fleet is greater than L is only 0.01. Give your answer to three decimal places.

The life span of a certain wood cutting machine manufactured by a factory has a normal distribution with a guarantee that any machine that stars malfunctioning within 36 months of the purchase will be replaced by a new one. How many percentages of machines are expected to be replaced in the following cases? Mean of 60 months and variance of 64 months2 Mean of 45 months and variance of 36 months2 Mean of 75 months and variance of 16 months2

Data originally from DASL http://lib.stat.cmu.edu/DASL/Datafiles/CancerSurvival.html (Links to an external site.). Some bronchial cancer patients had the following survival times (in days) after receiving a certain treatment: 20, 37, 63, 64, 72, 81, 138, 151, 155, 166, 166, 223, 245, 246, 450, 459.  (The second instance of “166” is not a mistake.) Do these numbers suggest that the average survival time, for all bronchial cancer patients who receive that treatment, is significantly different from 200 days? CANCER SURVIVAL Report an appropriate one-sample hypothesis test and use a 10% significance level. For Step 5 of the six-step process that was taught in this class, which would be the appropriate procedure and why?  Choose the correct option. Group of answer choices We would do a t-procedure because we have the standard deviation. We would do a t-procedure because the sample size is large. We would do a t-procedure because we do not have the population standard deviation and…

A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5 years, the child is administered an 1Q test. It is known that IQs are normally distributed with a mean of 100. If the IQs of the 20 children in the study result in a sample mean of 104.4 and sample standard deviation of 16, is there evidence that the children have higher IQs? Use the a= 0.10 level of significance. Complete parts (a) through (d). (a) Determine the null and alternative hypotheses. Ho: H = 100 Hy: H > 100 (b) Calculate the P-value. P-value = (Round to three decimal places as needed.) %3D Enter your answer in the answer box and then click Check Answer. 2 parts remaining Clear All Check Answer 80 888 112 F7 esc F4 F2 & @ %23 delete 7 8 9 2 3 4 { Q W E Y tab F G H K A D caps lock V B N M C - - .. .- つ くC N