Indicate how to show the sum of independent normal random variables is a normal random variable using moment generating functions
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given : Claim : on average, children tend to have more REM sleep than adults.
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: The formula for calculating the z- test statistic for two sample means is, The summary of the…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.20 hours per…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given : Claim : on average, children tend to have more REM sleep than adults.
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given that x1 = 2.6 σ1 = 0.6 n1 = 8 children x2 = 1.90 σ2 = 0.5 hour n2 = 8
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given, n1 = 11 n2 = 11x1= 2.7 x2= 2.20σ1 = 0.9…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given: n1 = 9, x1 = 2.9, s1 = 0.7 n2 = 9, x2 = 2.2, s2 = 0.5
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: The test statistic is obtained as below: z=x1¯-x2¯-μ1-μ2σ12n1+σ22n2 Here,…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: The sample mean and population standard deviation for the sample of 9 children are : x1 =2.9 hrsσ1…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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- Find third Central moment for poisson distribution around lambdaREM (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…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…Let Z be a st andard normal variable. Let mean and standard derviation > 0 be two real numbers. Then, the distribution of the random variableIs X=emean+standard derviation*Z called the Lognorma (mean,standard derviation) distribution. Write a function to generate random variables from this Lognormal distribution using a transformation method and generate a random sample of size n = 1000. Compare the histogram with the lognormal density curve given by dlnorm function in R.Use normal approximation to estimate the probability of getting less than 54 girls in 100 births. Assume that boys and girls are equally likely.
- Use normal approximation to estimate the probability of getting less than 46 girls in 100 births. Assume that boys and girls are equally likely.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 value
