The developer of an energy-efficient lawn mower engine claims that the engine will run continuously for 300 minutes on a single gallon of regular gasoline. Suppose a simple random sample of 50 engines is tested. The engines run for an average of 295 minutes, and the population standard deviation sigma is known to be 20 minutes. Test the null hypothesis that the mean run time is 300 minutes against the alternative hypothesis that the mean run time is not 300 minutes. Use a 0.05 level of significance.

It is known from past years that the average IQ of Commack elementary students is at least 110. The principal thinks that this is an overestimate, and that the average IQ of students here is less than 110. The principal administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 104 with a standard deviation of 10. Assume a significance level of 0.05 and conduct a hypothesis test. Calculate the test statistic.

One of the side effects of flooding a lake in northern boreal forest areas (e.g. for a hydro-electric project) is that mercury is leached from the soil, enters the food chain, and eventually contaminates the fish. The concentration in fish will vary among individual fish because of differences in eating patterns, movements around the lake, etc. Suppose that concentrations of mercury in individual fish follow an approximate normal distribution with a mean of 0.25 ppm and a standard deviation of 0.08 ppm. Fish are safe to eat if the mercury level is below 0.30 ppm. The Department of Fisheries and Oceans wishes to know the mercury level of the bottom 20% of the fish. The appropriate percentile and mercury level for this lake is:

A certain railway company claims that its trains run late 5 minutes on the average. The actual times (minutes) that 10 randomly selected trains ran late were provided giving a sample mean = 9.130 and sample standard deviation s = 1.4 . In testing the company's claim, (2-sided test) at the significance level of 0.01 and assuming normality the value of the test statistic and the critical values are, respectively:

Grades on a Chemistry test follow a normal distribution with a mean of 65 and a standard deviation of 12. Approximate the percentage of the students having scores below 50.

In a survey, three out of four students said that courts show too much concern for criminals. Find the probability that of seventy randomly selected students At most 56 feel that courts show too much concern

In a survey, three out of four students said that courts show too much concern for criminals. Of seventy randomly selected students Would 68 be considered an unusually high number of students who feel that courts are partial to criminals?

The probability of contracting a stomach virus while visiting Mexico is 60%. Find the probability that amongst 15 students visiting Mexico, Exactly five students contract a stomach virus:

The average growth of a certain variety of pine tree is 10.1 inches in three years. A biologist claims that a new variety will have a greater three year growth. A random sample of 25 of the new variety has an average three-year growth of 10.8 inches and a sample standard deviation of 2.1 inches. The appropriate null and alternate hypotheses to test the biologist's claim are:

The lifetime of a certain brand of heat pump is known to be normally distributed. A sample of 6 heat pumps yielded the following observations: 2.0 1.3 6.0 1.9 5.1 4 At a significance level of = .10 we will see if there is reason to believe that the mean life of the heat pumps is different from 2. Find the appropriate confidence interval for the true mean life of heat pumps. The sample standard deviation is 1.93

Of all the students applying for undergraduate studies, 13% applied to Honors college. Consider a randomly selected sample of 1500 students applying for undergraduate studies. Since we can view this as 1500 independent Bernoulli trials, this will be considered a binomial experiment. The mean of the binomial distribution is given by:

An industrial supplier has shipped a truckload of Teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these is "in excess" of the 12 ounces printed on each cartridge. To check this claim, a sample of n = 20 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: Sample mean = 12.11 Sample standard dev = .30 ounce To determine whether the supplier's claim is true, consider the test Ho: u = 12 vs. Ha: u >12, where u is the true mean weight of the cartridges. Find the critical value for this test. (No significance level provided in problem)

Consider the following probability mass function of a discrete random variable: X 1 2 3 4 5 P(X=x) 0.15 0.3 0.2 0.15 Find the missing value for P(4) if the above is to be a valid Probability Mass function.

It is known that 65% of Empire plan customers order their prescriptions via mail-order at least once a year. Suppose we randomly select 6 customers. What is the probability that exactly 4 of them have ordered via mail-order in the past year?

A local pharmacy wants to investigate the possibility of starting to deliver prescriptions to its senior clients on weekends, and decides to conduct a hypothesis test. The owner of the pharmacy has determined that the home delivery idea would be successful if the average time spent on the deliveries does not exceed 38 minutes. He has randomly selected 105 clients and has delivered their prescriptions to their homes. He conducts a hypothesis test, and finds the p- value for the test was .0742. Please state the correct conclusion:

Time magazine reported that 60% of young children have blood lead levels that could impair their neurological development. A sample of 10 children is randomly chosen. The probability that at least 8 children out of 10 in the sample may have a blood level that may impair development is:

The average monthly rent for Stony Brook students is = $732, with standard deviation of = $421 A random sample of 125 recent students is selected. The approximate probability that their average monthly rent payment will be more than $782 is:

If the confidence level is 90%, find the Margin of sampling error. The population is normally distributed, the sample size is 15 and the sample mean is 75 and the std. dev is 5.

For quality control purposes, the manufacturer of NFL footballs wishes to estimate the mean inflation pressure to within E = .015 lb of its true value with a 80% confidence interval. What sample size should be specified for the experiment? Use std. deviation = .1

The test statistic for a certain left sided hypothesis test is zo=.40. At the 10% significance level, which of the following is false?

The time that a skier takes on a downhill course has a normal distribution with a mean of 12.3 minutes and standard deviation of 0.4 minutes. The probability that on a random run the skier takes between 12.1 and 12.5 minutes is:

.3830

It can be shown that a certain distribution has a mean of 110 and a standard deviation of 20. What is the minimum percentage of the distribution between 80 and 140? Assume that nothing is known about the shape of the distribution -use Chebyshev's theorem.

In testing Ho: = 99 against Ha: 99 at the 10% level of significance, Ho is rejected if:

in a study that was performed to determine the # of vehicles using an intersection, the mean # was 375 vehicles per day and the standard deviation was 25 vehicles. Given that the distribution is symmetric and mound-shaped, what percent of the time is the # of vehicles using the intersection between 350 and 425?

What is the variance of (3X- 6Y) if X and Y are independent variables?

A Canadian railway company claims that its trains block crossings no more than 5 minutes per train on the average. Passengers feel that this time is much longer. The actual times (minutes) that 10 randomly selected trains block crossings were: 9.3 9.7 6.5 9.5 ......... 7.2 10.5 8.2 10.4 The sample mean = 9.130 and sample variance = 2.209. In testing this claim, at the significance level of 0.05 and assuming that the crossing times are normally distributed, the critical value and the test statistic are, respectively:

Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital will have to deal with eleven or more people who have contracted the disease?