When can we apply t-distribution?
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: The given data is as follows: For children, The sample size is 9, sample mean is 2.9 hours and the…
Q: Which discrete distribution has a difference between their means and variances equal to zero?
A: Ans- Which discrete distribution has a difference between their means and variances equal to zero ?
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Q: Show that the t-distribution with r = 1 degree of freedom and the Cauchydistribution are the same.
A: We have to prove that the t distribution with r=1 degree of freedom and the Cauchy distribution are…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Let, X1 and X2 be two random variables that are normally distributed with population means μ1…
Q: What is the level of significance? State the null and alternate hypotheses. (Enter != for ≠ as…
A: Let be the population mean sleep times for REM and non-REM respectively. Given that,Assume the…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: The random variable REM sleep follows normal distribution. There are two independent samples which…
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A: Let there are n trials and each having two outcomes - Success and Failure. The trials are…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
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Q: The number of accidents causing damages in an industrial setting are Poisson distributed with a mean…
A: Given:- The number of accidents causing damages in an industrial setting follows a Poisson…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: a. Level of significance The level of significance is defined as the probability of rejecting a null…
Q: REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that ?1 = 0.7 hour.…
A: Given that Sample size n1=8 Sample mean=2.9 hours Standard deviation σ1=0.7 Sample size (n2)=8…
Q: How are the t-distributions and z-distribution related? As sample size increases, what happens to…
A: Let X be the random variable from normal distribution with mean μ and standard deviation σ with…
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…
A: Given information: It is assumed that REM sleep time is normally distributed for both children and…
Q: The mean of Binomial distribution is 3 and variance is-. Find P(1 s x < 6)
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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: Perform a a Pearson’s correlation in SPSS to determine whether the weight of an automobile…
A: Note: Hi there! Thank you for posting the question. As the data corresponding to the variables…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: We have given that Sample size n1= 9b, n2=9 Sample mean xbar1 =2.9 , xbar2 = 0.5 Standard deviation…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Note:Hey there! Thank you for posting the question. Since there are multiple subparts are posted,…
Q: Use a t-distribution to answer this question. Assume the samples are random samples from…
A: The degree of freedom for the difference in the sample means for two population is, df=n1+n2-2…
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: As the number of degrees of freedom for a t distribution increases, the difference between the t…
A: What happened if the deg. of freedom for a t-distribution increases?
Q: EM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: For Children : Mean , x1 = 2.5 Population standard deviation , σ1 = 0.7 For Adults : Mean , x2 =…
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…
Q: True or false Ć Stochastic approximation is the same as sample average approximation.
A: To Explain : Stochastic approximation is the same as sample average approximation is it true or…
Q: Find (or estimate) the P-value. (Round your answer to four decimal places.) b) Sketch the sampling…
A: For children, Sample size n1 = 9, sample mean = 2.9, population SD = 0.7 For adults, Sample size n2…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given: n1=11, X1=2.5, σ1=0.6n2=11, X2=1.8, σ2=0.7α=0.01
Q: Fail to reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for…
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Q: A survey was conducted where 27 students were asked which social media app is their favorite,…
A: 1) The table is Male Female Total Twitter 4 4 8 Tiktok 4 15 19 Total 8 19 27 The…
Q: A random variable x follows Poisson distribution with an average rate of 6, Find p(x=3) =…
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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: M (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: We have given that Sample sizes n1=9 ,n2 =9 Sample means xbar1 =2.6 ,xbar2 = 1.70 and sigma1= 0.6…
Q: e is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years…
A: The level of significance is given as α = 0.10(=10%). Hypotheses for the test are given below: Test…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Sampling distribution: Since population standard deviations are known, the appropriate test is…
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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: The Poisson distribution is a continuous distribution which is very useful in solving waiting time…
A: False The Poisson distribution is the discrete distribution which very useful in solving the waiting…
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A:
Q: REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…
A: Given data is appropriate for testing of hypothesis to test t-test for difference of means . because…
When can we apply t-distribution?
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- The averate rate of x is 2. Using Poisson distribution, Calculate p(x = 1)?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…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 = 0.8 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.40 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…
- Does T-distribution have asymptotic tails?How can I solve this ?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…True or falseREM (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
