Exam 9: Hypothesis Testing: Single Population

The Next Questions Are Based On The Following Information: An accountant claims to be able to complete a standard tax return in under an hour.For a random sample of 24 tax returns,the accountant averaged 63.2 minutes with a standard deviation of 7.7 minutes. -What is the test statistic for this test?

A local transportation planning group is concerned about the lack of car-pooling on the part of commuters.They are afraid that the proportion of local drivers car-pooling is below the national average of 15%.A survey of 400 local drivers reveals that 12.22% of them car pool.Is there evidence that the actual proportion of local commuters car-pooling is less than 15%? Test at the 10% level of significance.

Explain the hypothesis test of the population proportion for large sample sizes.

Match the symbol (1 - β)with the correct definition.

The Next Questions Are Based On The Following Information: The dean of a business college in the Midwest claims that he can correctly identify whether a student is a finance major or a music industry management major by the way the student dresses.Suppose in actuality that he can correctly identify finance majors 84% of the time,while 16% of the time he mistakenly identifies a music industry management major as a finance major.Presented with one student and asked to identify the major of this student (who is either a finance or music industry management major),the dean considers this to be a hypothesis test with the null hypothesis being that the student is a finance major and the alternative that the student is a music industry management major. -An assembly line will be shut down for maintenance if the defect rate exceeds 2.3%.Suppose you adopt a 5% significance level and take a random sample of 200 items from the assembly line and compute the proportion of defective items.For what values of the sample proportion will the assembly line be shut down?

An alternate hypothesis is a statement about a population parameter that is accepted only when the null hypothesis is rejected.

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. -What is the appropriate decision rule?

An assembly line will be shut down for maintenance if the defect rate exceeds 4.6%.Suppose you adopt a 5% significance level and take a random sample of 375 items off the assembly line and compute the proportions that are defective.For what value of the sample proportion will the assembly line be shut down?

If the null hypothesis is H₀ : μ = 100,and you know that = 105 and = σ / = 2.5,then the test statistic value is Z = 2.

The Next Questions Are Based On The Following Information: An engineering research center claims that,through the use of a new computer control system,automobiles should achieve,on average,at least an additional 5 miles per gallon of gas.A random sample of 81 automobiles was used to evaluate this product.The sample mean increase in miles per gallon achieved was 4.5,and the sample standard deviation was 2.9 miles per gallon. -State the appropriate null and alternative hypotheses.

A null hypothesis is rejected at the 0.025 level,but is not rejected at the 0.01 level.This means that the p-value of the test is between 0.01 and 0.025.

The Next Questions Are Based On The Following Information: The manufacturer of a new chewing gum claims that at least 80% of 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 200 dentists indicate that 74.1% of the respondents do actually prefer their gum. -If conducting a two-sided test of population means,unknown variance,at level of significance 0.05 based on a sample of size 20,the critical t-value is:

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 are the appropriate null and alternative hypotheses?

When testing the mean of a normal population,the Z test is always used.

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 was 11.6 minutes.Is there evidence that the average amount of time required to assemble a component is something other than 14 minutes? Use α = 0.01.

The Next Questions Are Based On The Following Information: Consider a problem with the hypothesis test H₀ : μ = 4 against H₁ : μ > 4,and the following decision rule: Reject H₀ if > 1.645 -Compute the probability of Type II error and the power of the test for μ= 4.06.

The power of a test is inversely related to the probability of a Type II error.

The Next Questions Are Based On The Following Information: Manufacturing planning wants to estimate plant capacity in order to schedule customer orders and improve on-time delivery.A random sample of ten days output gave the following results for numbers of finished components produced: 577,642,615,655,600,570,640,620,595,and 575.Planning is concerned about the variability of daily output and views as undesirable any variance above 525. -Test at the 10% significance level the null hypothesis that the population variance for daily output does not exceed 525.

The probability of rejecting the null hypothesis when the null hypothesis is false is known as the power of the test.

Provide the test for mean of a normal distribution with population variance unknown,with the null hypothesis H₀ : μ ≤ μ₀