Exam 9: Hypothesis Testing: Single Population

The Next Questions Are Based On The Following Information: A pharmaceutical manufacturer is concerned that the mean impurity concentration in pills should not exceed 3%.It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation 0.4%.A random sample of 36 pills from a production run was checked,and the sample mean impurity concentration was found to be 3.09%. -How is hypothesis testing used in problems that have high variance levels?

The Next Questions Are Based On The Following Information: A professor claims that the average score on a recent exam was 83.Suppose you want to test whether the professor's statement is correct.Assume that the test scores are normally distributed.You ask some people in class how they did,and record the following scores: 82,77,85,76,81,91,70,and 82. -Which of the following is the most accurate statement about the p-value?

The Next Questions Are Based On The Following Information: The supervisor of a production line believes that the average time to assemble an electronic component is 14 minutes.Assume that assembly time is normally distributed with a standard deviation of 3.4 minutes.The supervisor times the assembly of 14 components,and finds that the average time for completion is 11.6 minutes. -Which of the following statements is most accurate?

The Next Questions Are Based On The Following Information: The state lottery office claims that the average household income of those people playing the lottery is at least $37,000.Assume that the distribution of household income of those people playing the lottery is normally distributed with a standard deviation of $5,756.Suppose that for a sample of 25 households,it is found that the average income was $36,243. -What is the most accurate estimate of the p-value?

The Next Questions Are Based On The Following Information: An insurance company employs agents on a commission basis.It claims that in their first year,agents will earn a mean commission of at least $42,000 and that the population standard deviation is no more than $6,800.A random sample of nine agents found,for commissions in the first year, and The population distribution can be assumed to be normal. -Calculate the sample mean and sample standard deviation.

The Next Questions Are Based On The Following Information: The sales representative for a manufacturer of a new product claims that the product will increase output per machine by at least 29 units per hour.A line manager installs the product on 15 of the machines,and finds that the average increase was only 26 with a standard deviation of 6.2. -The value of the test statistic is:

How is the power of a test connected to the decision rule in hypothesis testing?

When testing whether a population proportion is zero,a t test can be used only if the sample size is large.

Explain the relationship between Type I error and Type II error in a hypothesis test.

If a random sample of size n is drawn from a normal distribution,then the standardized variable t = ( - μ)/ (s/ )has a Student's t-distribution with n-1 degrees of freedom.

Match the symbol α with the correct definition.

The manufacturer of a new chewing gum claims that at least eight out of ten dentists surveyed prefer their type of gum and recommend it for their patients who chew gum.An independent consumer research firm decides to test their claim.The findings in a sample of 400 doctors indicate that 76% do actually prefer their gum.Is this evidence sufficient to doubt the manufacturer's claim? Use α = 0.05.

The Next Questions Are Based On The Following Information: A hydraulic press is operating correctly when the standard deviation of the pressure is less than 120 pounds-per-square-inch (psi).Suppose you take a random sample of 15 measurements throughout the day of the psi and find the standard deviation to be 148.Suppose you want to test whether the press is operating correctly. -Assume the following null and alternative hypotheses: H₀ : μ = μ₀ and H₁ : μ > μ₀.In addition,you know σ.Take a random sample of n observations and choose some value α.What is the decision rule for this test?

A professional rock climber claims that he can climb a particular mountain within half an hour.From a random sample of 20 attempts,the rock climber averaged 33.3 minutes with a standard deviation of 3.9 minutes.Is there sufficient evidence to suggest that the climber's claim is incorrect at a significance level of 10 per cent?

The manufacturer of a new product claims that his product will increase output per machine by at least 38 units per hour.A line manager adopts the product on 18 of his machines,and finds that the average increase was only 35 units per hour with a standard deviation of 12.2 units.Is there evidence to doubt the manufacturer's claim at a significance level of .10?

The Next Questions Are Based On The Following Information: An alcohol brewery firm claims that the proportion of alcohol in their new drink is at most 10 percent.A random sample of 100 bottles of the drink were selected and found to consist of 9 percent alcohol. -What is the value of test statistic for this sample?

A professor of statistics wants to test that the average amount of money a typical college student spends per day during spring break is over $70.Based upon previous research,the population standard deviation is estimated to be $17.32.The professor surveys 35 students and finds that the mean spending is $72.43.Which of the following statements is most accurate?

The Next Questions Are Based On The Following Information: The sales representative for a manufacturer of a new product claims that the product will increase output per machine by at least 29 units per hour.A line manager installs the product on 15 of the machines,and finds that the average increase was only 26 with a standard deviation of 6.2. -What are the appropriate null and alternative hypotheses?

The Next Questions Are Based On The Following Information: A team of builders has surveyed buyers of their new homes for years.Consistently,only 41% of the buyers have indicated that they were "quite satisfied" or "very satisfied" with the construction quality of their homes.The builders have implemented new procedures and adopted a revised quality-inspection system to ultimately improve customer satisfaction.They have surveyed 104 buyers since implementing changes;these buyers seem representative,with no systematic changes from past purchasers.Of the 104 buyers,52 indicated they were quite or very satisfied. -Calculate the appropriate statistic for testing the null hypothesis.

The Next Questions Are Based On The Following Information: A hydraulic press is operating correctly when the standard deviation of the pressure is less than 120 pounds-per-square-inch (psi).Suppose you take a random sample of 15 measurements throughout the day of the psi and find the standard deviation to be 148.Suppose you want to test whether the press is operating correctly. -What can be concluded by failing to reject the null hypothesis?