Let x be the mean of random sample size (n) from distribution N(u, 10). Such as P(x- 1
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A: We need to show that:-
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: 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…
A: We have given that Sample size n1= 9b, n2=9 Sample mean xbar1 =2.9 , xbar2 = 0.5 Standard deviation…
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A: Given Population size= 12, 6, 24, 30, 18 sample size=2
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
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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=11, X1=2.5, σ1=0.6n2=11, X2=1.8, σ2=0.7α=0.01
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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
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Q: he average wait time to get seated at a popular restaurant in the city on a Friday night is 12…
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- The weights of all the turkeys sold in Fairfax County in 2020 were recorded in the data set “Fairfax Turkey Weights” found in the table with the column labeled "Weight". The weights are presented in pounds. There are 235,428 turkeys in this population. Does the mean calculated in the table with the column labeled "Sample (Weight)" come from a sampling distribution that is approximately Normal? Check all three conditions of the Central Limit Theorem using one complete sentence for each condition to answer this question.The average wait time to get seated at a popular restaurant in the city on a Friday night is 11 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 15 randomly selected men who were wearing a tie are shown below Assume that the distribution of the population is normal. 11,9,9, 12, 11, 10, 12, 13, 9,9, 11, 13, 12, 9,9 What can be concluded at the the α 0.01 level of significance level of "-? S1 canc a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: C. The test statistic ? ' - please show your answer to 3 decimal places.) d. The p-value = Please show your answer to 4 decimal places.) e. The p-value is?a f Based on this, we should Select an answer g Thus, the final conclusion is that the null hypothesis. The data suggest the populaton mean is significantly more than 11 at a = 0.01, so there is statistically significant evidence to conclude that the population mean wait time for men who wear a tie is more than 11…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…
- Suppose that the time spent by children in front of the television set per year has the distribution N(1500, 250) What proportion of children spend less than 1000 hours in front of the television?To test the null hypothesis that the difference between two population proportions is equaluse StatCrunch or the formulaz =(p1 (carat) - p2 (Carat) / (Sq root) p1 (carat) (1 - p1 (carat)/n1 + p2(carat) (1 - p2(carat))/n2As long as n1 and n2 are both large, the sampling distribution of the test statistic z will beapproximately the standard normal distribution. Given the sample data below, test the claim that the proportion of female voters who plan to vote Republican at the next presidential election is less than the percentage of male voters who plan to vote Republican. Use the traditional method of hypothesis testing and use a significance level of 0.05.Men: n1 = 250, x1 = 146, p1(carat)=.584Women: n2 = 309, x2 = 103, p2(carat) = .333 3)a. Write the null and alternative hypotheses to test this claim. b. What is the value of the test statistic? Show you work.c. What is the associated P-value? d. State your conclusion and explain in context using ΅ = 0.05.please only do: if you can teach explain each
- 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…Let X be a random variable with a uniform distribution over the interval [-3,6]. Determine the mean of X. [The answer should be a number rounded to five decimal places, don't use symbols such as %]A local DMV (location of your choice) wanted to assess the number of mistakes that were made by its operators (aka clerks). One hundred samples were gathered from each of 20 operators (note: n = 100 for calculation of σp but you will need 100 * 20 to calculate p-bar). The results are shown in the table below. The DMV wants to set control limits to include 95% of the random variation. Operator # Number of errors Fraction defective Operator # Number of errors Fraction defective 1 6 11 6 2 5 12 1 3 0 13 8 4 1 14 7 5 4 15 5 6 2 16 4 7 5 17 11 8 3 18 3 9 3 19 0 10 2 20 4 Calculate p-bar and σp. Complete the fractions defective in chart. Compute the control limits and center line for a p-chart. Plot the fraction defective in a p-chart and decide if the performance of the operators is…
- 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 valueIf the grades of students in Principles of statistics are distributed through the N ( 60 , 100 ) , then the percentage of students with grades between 65 and 70The average wait time to get seated at a popular restaurant in the city on a Friday night is 10 minutes. Is the mean wait time less for men who wear a tie? Wait times for 15 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 7, 10, 11, 9, 11, 7, 8, 11, 9, 9, 11, 9, 11, 9, 7 What can be concluded at the the α = 0.10 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H0: H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly less than 10 at α = 0.10, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is equal to 10.…