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 forboth 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 a₁ = 0.7 hour. Another random sample of n₂ = 9 adults showedthat they had an average REM sleep time of X₂ = 2.00 hours per night. Previous studies show that o₂ = 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?State the null and alternate hypotheses.O Ho: H₁H₂i H₂i H₂> H₂O Ho: H₁ H₂i H₂i H₂ What is the value of the sample test statistic? (Test the difference ₁-₂. Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)Sketch the sampling distribution and show the area corresponding to the P-value.0-3-2 -1 0 1 2Read It-2-1 031 2Watch It0-30-3(d) Based on your answers in parts (a) to (c), 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 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 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.0-33-2-1-20 1 2-1 0 132(e) Interpret your conclusion in the context of the application.O 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 sufficient 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.Need Help?3

The random sample of children, The average REM sleep time, hours per nightThe population standard…

Answered: REM (rapid eye movement) sleep is sleep…

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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Help me answer questions in picture with the following information below: 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 ?1 = 0.7 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.00 hours per night. Previous studies show that ?2 = 0.9 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance.
You are studying memory in zebra fishes by allowing one group of fish (n = 6) to practice a maze while the other group is the control and do not get practice sessions (n = 5). A month after the practice sessions, you test the time it takes the fish to solve the maze. If the fish remember the maze, they should be faster. QQ plots show long-tailed distributions. Choose the best type of test of two means to assess this research question Two-sided Mann Whitney U test One-sided paired t-test One-sided unpooled variance t-test Two-sided unpooled variance t-test O One-sided Mann-Whitney U test O One-sided pooled variance t-test
A psychologist obtains a random sample of 30 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 45 minutes each day until they give birth. We know that IQs are normally distributed with a mean of 100. A few years after their births the children were given an IQ test and the IQs of the 30 children in the study resulted in a sample mean of 104.2. Assume the population standard deviation for IQ of children is 15. Is there evidence that the children who listen to Mozart for at least 45 minutes each day during pregnancy have higher IQs at the 0.05 level of significance? Step 1: Define the parameter & setup the testStep 2: State the Level of SignificanceStep 3: Find the value of the Test StatisticsStep 4: Find P-Value OR Find Critical ValueStep 5: State Conclusion and why
Researchers were interested in assessing whether stress levels at the beginning of the semester are related to (i.e., correlated with) stress levels during finals week. To test this, stress was measured in 5 students at the start of the semester and then again at the end of the semester during finals week. Participant Stress 1 Stress 2 (X - MX) (Y - MY) (X - MX) (Y - MY) (X - MX)2 (Y - MY)2 1 22 22 -4.4 -6 2 32 34 5.6 6 3 24 25 -2.4 -3 4 28 30 1.6 2 5 26 29 -0.4 1 What is the observed correlation coefficient (i.e., r value)?
Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the…
Check my An airline's data indicate that this past year, the average time it takes to board their flights is 45 minutes. The airline is considering changing their boarding procedures to reduce the boarding time for travelers. The new procedures were implemented and the boarding times for a random sample of 22 customers was taken to determine if there was a statistically significant decrease at in boarding times a= 0.10 with z = - 0.89 and t = . 1.07. What is the decision?
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…
A certain city the Transportation Authority (CTA) has trollies leaving regularly throughout the day beginning at 5:00 a.m. Although the length of a trip and the number of stops are constant, the time taken for each trip varies due to weather, traffic, and time of the day. According to the CTA, the mean time taken for the trip is 50 minutes. Suppose the travel time is Normally distributed with standard deviation o = 4 minutes. A random sample of 25 trips is obtained, and the time for each is recorded. Find the probability that the sample mean time will be less than 48 minutes.
Kelsi is curious to see if ST 243Z campus students typically got their first cell phone at a younger age than they (Kelsi) got their first phone. To investigate this, they take a random sample of 20 students from all ST 243Z campus students this Winter 2024 term and find those students had an average age of 11.85 years when they reported receiving their first phone. The standard deviation of the population, ox, is known to be 1.91 years. The histogram and boxplot of the sample are provided below. We are interested at exploring at the 90% confidence level. What is the average age for getting their first phone of all ST 243Z campus students in Winter 2024? 8 9 Age when got first phone 10 11 12 Age (years) 13 14 15 8 9 Age when got first phone T 10 11 12 Age (years) T 13 T 14 T 15 1. In 1-3 sentences, describe the distribution of the sample, including shape, center, spread, context, and outliers (if relevant).
An elephant eats an average of 3 bushels of alfalfa per day, with a standarddeviation of 0.8 bushels. Suppose that you need to feed 10 elephants for oneweek. If the distribution is normal, what is the minimum number of bushels ofalfalfa so that there is no more than a 10% chance of running out by the end of the week?
Suppose a researcher is interested in the effectiveness of a new novel talk therapy technique in reducing overall depression as identified via score report on the geriatric depression scale (GDS). In order to carry out this hypothesis, the researcher gathers a SRS of participants in the program and performs the GDS test prior to, and after initiation of the new therapy technique. Assume the SRS score report presented below represents an approximately normal distribution. Participant GDS Score (Out of 15) Prior to intervention GDS Score (Out of 15) Following intervention A 12 8 B 13 7 C 12 7 D 14 9 E 11 6 F 11 7 A) What type of study design is this? B) Conduct a paired sample t test investigating the effectiveness of the new therapy technique with 95% confidence. Write out your null and alternative hypotheses, and interpret your pvalue correctly. C) Construct a 95% confidence interval representing the average difference…
On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 7 trials of this experiment. 541, 800, 667, 362, 542, 667, 800 Send data to calculator (a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place. 1 2 (b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable. zero modes one mode: 0 O two modes: and ?

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