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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.
However, you understand that pitfalls may exist in the data collection process and the reasoning process. For instance, you know to watch for:
Employees in a large computer firm claim that the mean salary of the firm's programmers is less than that of its competitors. The competitor's salary is $47,000. A random sample of 30 of the firm's
Find the test statistic for the following proportion: A collection of 500 randomly selected teachers revealed that 61% felt that all students should be required to take algebra in high school. Show
Find the minimum sample size that should be chosen to assure that the proportion estimate p will be within the required margin of error, .06. Use a 95% confidence interval and a population proportio
An employee of bank wants to test the null hypothesis that on average the bank cashes 10 bad checks per day against the altenative that this figure is too small. If he takes a random sample and dec
What is the set of null and alternative hypothesis if we want to determine whether the mean salary of male and female employees is the same?
Business firm makes and sells a steel product. Product costs $5 to produce. Product sells for $20. Product requires 4 pounds of steel to make. Firm has 100 pounds of steel. Determine the number of u
Joe used a project management software package and has determined the following results for a given project. Expected completion time of the project = 22 days Variance of project Completion time = 2
Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $44 and the es
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean = 7500 and estimated s
How would you go about selecting a particular level of significance (α) to conduct a hypothesis test? Provide two considerations that might be useful in guiding your choice.
A biologist wants to test the null hypothesis that the mean mean wingspan of a certain kind of insect is 12.3mm against the altenative that it is not 12.3 mm.
Directional and nondirectional hypotheses can be easily interchanged according to the hypothesis the researcher is testing. For instance, a drug company might predict that a drug will help a subject
A botanist wishes to test the null hypothesis that the average diameter of the flowers of a particular plant is 9.6cm. He decides to take a random sample of size n=80 and accept the null hypottesis
The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of twelve motors was tested, and it was found that th
What is the value of the sample test statistic? (Round your answer to two decimal places.) Find the P-value. (Round your answer to four decimal places.)
If 9 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 73.6 mosquitos per square meter. Assume that the variable is normally
The mean weight of loads of rock is 49.0 tons with a standard deviation of 12.0 tons. If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is
Test the hypothesis that the average price is higher than $2.57. Use level of significance a = 0.05.
A charity receives 1700 contributions. Contributions are assumed to be independent and identically distributed with mean 2945 and standard deviation 150. Calculate the approximate 90th percentile fo
Suppose a manufacturing company makes a certain item. The time to produce each item is normally distributed around a mean of 157 minutes with a standard deviation of 46 minutes.
Suppose an x distribution has mean μ = 4. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81.
1. In a recent survey of 4513 college undergraduates, 20% reported having fallen asleep in class. To test this result, your instructor sampled 25 students from his class and asked them if they
If when determining the cross-products for your correlation coefficient, positive z scores on one variable go with negative z scores on the other variable and negative z scores on one variable go wi