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Question
For a given significance level, increasing the sample size will tend to increase the chi-square critical value used in testing the null hypothesis about a population variance.Answer
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A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. The following chart shows some of the results of the ANOVA computations; however, some of the output is missing. Given what is available, the proper conclusion to reach based on the sample data is that the population means could be equal using a 0.05 level of significance.
ANOVA: Single Factor
Q:
In one-way analysis of variance, the within-sample variation is not affected by whether the null hypothesis is true or not.
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In a one-way analysis of variance test, the following null and alternative hypotheses are appropriate:
H0 : μ1 = μ2 = μ3
Hα : μ1 ≠μ2 ≠μ3
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In conducting one-way analysis of variance, the sample size for each group must be equal.
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In a one-way analysis of variance design, there is a single factor of interest but there may be multiple levels of the factor.
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Q:
In performing a one-tailed test for the difference between two population variances, which of the following statements is true?
A) The level of alpha needs to be doubled before finding the F-critical value in the table.
B) The sample variance that is predicted to be larger in the alternative hypothesis goes in the numerator when forming the F-test statistic.
C) You always place the larger of the two sample variances in the numerator.
D) The alternative hypothesis must contain the equality.
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The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given: Old Seed
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Q:
If a hypothesis test for a single population variance is to be conducted, which of the following statements is true?
A) The null hypothesis must be stated in terms of the population variance.
B) The chi-square distribution is used.
C) If the sample size is increased, the critical value is also increased for a given level of statistical significance.
D) All of the above are true.
Q:
When conducting a one-tailed hypothesis test of a population variance using a sample size of n = 24 and a 0.10 level of significance, the critical value is:
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B) 35.1725
C) 33.1962
D) 36.4150
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A frozen food company that makes burritos currently has employees making burritos by hand. It is considering purchasing equipment to automate the process and wants to determine if the automated process would result in lower variability of burrito weights. It takes a random sample from each process as shown below. Process 1 (by hand)
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In a two-tailed hypothesis test involving two population variances, if the null hypothesis is true then the F-test statistic should be approximately equal to 1.0.
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One of the major automobile makers has developed two new engines. At question is whether the two engines have the same variability with respect to miles per gallon. To test this, the following information is available: Engine 1Engine 2n1 = 7n2 = 91 = 28.72 = 33.4s1 = 3.4s2 = 4.12Based on this situation and the information provided, the appropriate null and alternative hypotheses are:H0 : Ha : =
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The managers for a vegetable canning facility claim the standard deviation for the ounces per can on the new automated line is less than for the older manual line. Given this, the correct null and alternative hypotheses for performing the statistical test are:H0 : 1 = 2Ha : 1 2
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A potato chip manufacturer has two packaging lines and wants to determine if the variances differ between the two lines. They take a sample of n= 15 bags from each line and find the following: The value of the test statistic is F = 1.5
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In a hypothesis test involving two population variances, if the null hypothesis states that the two variances are strictly equal, then the test statistic is a chi-square statistic.
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When using a chi-square test for the variance of one population, we are assuming that the population is normally distributed.
Q:
Assume a sample of size n = 12 has been collected. To perform a hypothesis test of a population variance using a 0.05 level of significance, where the null hypothesis is:H0: 2 = 25The upper tail critical value is 21.92.