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##### Problem Set A Hypothesis testing for the mean (z and t tests)

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Question;Problem Set A;Hypothesis;testing for the mean (z and t tests);1. Phone calls received by a Police dept. are normally;distributed. A random sample of 16 days showed that the dept. received an;average of 223 phone calls per day with a sample standard deviation of 31;calls.;a. Find a 95% confidence;interval for the mean number of phone calls received each day.;b. Find the margin of;sampling error E;c. Find the length of;the confidence interval;d. Find a point estimate;for the mean.;e. Use the;confidence interval found in (d) to test whether the mean # of phone calls received is 205.;f. Use the;confidence interval found in (d) to test whether the mean # of phone calls;received is 220;g. Without;computing the 99% CI, can you draw a conclusion (still testing whether the mean;# of phone calls is 220) at the 1% significance level?;h. Without;computing the 99% CI, can you draw a conclusion (now testing whether the mean #;of phone calls is 205) at the 1% significance level?;2. The average length of a new born baby is 20 inches with a;standard deviation of 1 inch.;a.;If n=100, what is the mean of the sampling;distribution of means?;b.;If n=100, what is the standard deviation of;the sampling distribution of means?;c.;What is the probability that the;mean height of a random sample of 100 babies is more than 20.2 inches?;3. A psychologist;claims that the mean age at which children start talking is 12.8 months.;Carlos wanted to check if this claim is true. He took a random sample of;20 children and found that the mean age at which these children started talking;was 13.9 months with a standard deviation of 1.8 month. Using the;5% significance level, can you conclude that the mean age at which all children;will start talking is different from 12.8;months? Assume that the ages at which all children start talking have an;approximately normal distribution.;a.;How many degrees of freedom will you use for this problem?;b.;Find the critical values for this hypothesis test;c.;Find the test statistic to.;d.;Find the p-value for this test;e.;Use the p-value to draw a conclusion.;f.;Find the 95% confidence interval for the mean age at which all children;start talking.;g.;Use the confidence interval to test whether the mean age at which;children start talking is 12.8 months.;4.;Before bidding on a contract, a contractor wants to be 90% confident;that he is in error by less than 20 minutes in estimating the average;time it takes a certain kind of cement to dry. If the standard deviation;of the time it takes to dry can be assumed to be 75minutes, on how;large a sample should he base the estimate?;5. The weights of a fish in a certain pond;that is regularly stocked are considered to be normally distributed with a mean;of 3.1 pounds and a standard deviation of 1.1 pounds. A random sample of size;30 is selected from the pond and the sample mean is found to be 2.4 pounds. Is;there sufficient evidence to indicate that the mean weight of the fish differs from 3.1 pounds? Use a 10% level of;significance.;6.;Green Line, a major discount stock brokerage in Canada, claims that customers;calling in to make trades on the stock market are left on hold for an average;of about 22 seconds. Suppose that an account executive was concerned about the;satisfaction level of the clients and selected a random sample of 100 traders;who phoned. The length of time that a client was left on hold was recorded.;Assume that the sample mean was 23.5 seconds with a standard deviation of 8;seconds.;a.;Is there sufficient evidence to;indicate that customers are left on hold for an average length of time greater than 22 seconds? Use a 5% level of;significance.;b.;Estimate the p-value for this test.;c.;Based on the p-value will you reject;Ho at the 5% significance level?;d.;Would you reject Ho if the;significance level were changed to 2.5%?;7. The senior executive of a publishing firm;would like to train employees to read faster than 1000 words per minute. A;random sample of 21 employees underwent a special speed reading course. This;sample yielded a mean of 1018 words per minute with a standard deviation of 30;words per minute. Do the data support the belief that the speed-reading course;will enable the employees to read more than;1000 words per minute at a significance level of 0.05? Assume that reading;speeds of persons who have taken the course are normally distributed.;a. How many degrees of freedom will you use?;b. Draw the null distribution and include the;critical values and the test statistic.;c. Estimate the p-value for this test to draw a;conclusion at the 5% significance level;8. A manufacturer of strapping tape claims that the tape;has a mean breaking strength of 500 psi. Experience has shown that breaking;strengths are approximately normally distributed, with a standard deviation of;48 psi. A random sample of 16 specimens is drawn from a large shipment of tape;and a mean of 480 psi is computed. Can we conclude from these data that the;mean breaking strength for this shipment is less than;that claimed by the manufacturer? Let alpha = 0.05.;a. Will you use z or;t?;b. Find the critical;value and the test statistic.;c. Find the;p-value. What is your conclusion?;9.;The mean length of time required to;perform a certain assembly-line task at Wharton Electronics has been;established at 15.5 minutes, with a standard deviation of 3 minutes. A random;sample of 9 employees is taught a new method. After the training period, the;average time these 9 employees take to perform the task is 13.5 minutes. Do;these results provide sufficient evidence to indicate that the new method is faster than the old?;Let alpha = 0.05. Assume that the times required to perform the task are;normally distributed.;a.;What side is this test.;b.;Find the critical value and the test;statistic;c.;Find the p-value. What is your conclusion?;10.;A certain type of yarn is;manufactured under specifications that the mean tensile strength must be 20;pounds. A random sample of 16 specimens yields a mean tensile strength of 18;pounds and a standard deviation of 3.2 pounds. Can we conclude from these data;that the mean tensile strength for the population is less;than 20 pounds? Assume that the tensile strengths are approximately;normally distributed. Let alpha = 0.05.;a.;Draw the null distribution;including the critical value and the test statistic;b.;Estimate the p-value;c.;What is the conclusion?;11.;We are performing a two sided t;test. ?o=10, to=2, n=14;a.;Estimate the p-value for this two;sided test.;b.;What is your conclusion at the 5%;significance level?

Paper#61430 | Written in 18-Jul-2015

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