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 = 2.00 hours per night. Previous studies show that σ2 = 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. 1. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.) 2. Find (or estimate) the P-value. (Round your answer to four decimal places.)

70 million pounds of trout are grown in the U.S. every year. Farm raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 38 farm raised trout is selected. The mean fat coherent for the sample is 30.5 grams per pound. Find the probability of observing a sample mean of 30.5 grams of fat per pound or less in a random sample of 38 farm raised trout. Carry intermediate computations to 4 places and your answer to 3

Assume that the square footage of a residential house in the US is normally distributed with a mean=1000 and standard deviation=150 square feet. If we select a random house what is the probability that it will be at most 1050 square feet?

The 3-point shooter star of your favourite team usually attempts twelve 3-point shots in a basketball game. The team record shows that the shooter makes 45% of all 3-point shots attempted in a game. Assuming that the shots are independent of each other,what is probability that the star will make shots at least 2 standard deviation more than the expected?

Samples are drawn from a population with mean 144 and standard deviation 43. Each sample has 12 randomly and independently chosen elements. Find the mean, uz, of the distribution of sample means.

The University of Montana admission standards require students to have an ACT score of at least 22.We know that Montana ACT scores are normally distributed with a mean of 20.1 and standarddeviation of 4.  If we ask a random sample of 100 students who took the ACT, how many would be expected toqualify for admission to UM?

Does playing Mozart for unborn babies result in having children with higher IQs?    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? Use the p-value approach. a. Define the parameter we are testing and setup a hypothesis test to see if the mean IQ of children who listened to Mozart at least 45 minutes a day during pregnancy is higher than the national mean of 100: b. Calculate the test statistics for this…

The authors of the paper "Length of Stay, Wait Time to Surgery and 30-Day Mortality for Patients with Hip Fractures After Opening of a Dedicated Orthopedic Weekend Trauma Room"† were interested in estimating the mean time that patients who broke a hip had to wait for surgery after the opening of a new hospital facility. They reported that for a representative sample of 204 people with a fractured hip, the sample mean time between arriving at the hospital and surgery to repair the hip was 28.5 hours and that the sample standard deviation of the wait times was 16.8 hours. If we had access to the raw data (the 204 individual wait-time observations), we might begin by looking at a boxplot. The authors of the paper commented that there were several outliers in the data set, which might cause us to question the normality of the wait-time distribution, but because the sample size is large, it is still appropriate to use the t confidence interval. We can use the confidence interval of this…

An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.55 ppm and a standard deviation of 3 ppm. Suppose that you draw a random sample of 12 printers. Part i) Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 18.15 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion) ...

A report on egg consumption shows that people living in China eat an average of 196 eggs each year with a standard deviation of 18.3 eggs.  If a group of 81 Chinese people are selected at random, what is the probability that the average egg consumption of this group will be more than 200 eggs?