Exam 13: Chi-Square Applications

Biology A biology professor claimed that the proportions of grades in his classes are the same.A sample of 100 students showed the following frequencies: Grade F Frequency 18 20 28 23 11 -In a hypothesis test for the population variance,the alternate hypothesis is the population variance is greater than 17.0.The significance level to be used is 0.025 and the sample size to be taken is 25.What table value should we use from the chi-square distribution?

Accommodations Business travelers stay in a variety of accommodations.A set of national percentages for types of accommodations shows their choices below.During a sluggish economy there may be changes in business traveler accommodation patterns so a travel consultant surveyed 300 business travelers and asked about their accommodations.These data will be used to test whether or not the present accommodation distribution is the same as the national one. Accommodations Percent Frequency Hotel or Motel 64 186 Cabin, Condo, or Vacation Home 17 45 Stayed with Friends and Relatives 14 57 Other 5 12 -What is the conclusion?

TV Model Three hundred individuals were asked to view the picture quality of four different TVs and asked to choose the one they preferred.The data is shown in the following table: TV Madel Number Wha preferred A 73 D Tatal 300 -Test the equality of proportions at the 0.05 level the hypotheses. Compute the test statistic.

Employee Four employees are monitored to determine whether there is any difference in the proportions of acceptable parts produced by the employees.The sample of parts produced is given below. Employee Quality Total Acceptable 265 270 225 180 950 Unacceptable 10 5 15 20 50 Total 275 275 250 200 1000 -These data provide the information for testing the hypothesis that the proportion of unacceptable is the same for the four employees.Calculate the test statistic.

Stocks One thousand stocks watched by a financial advisory company are advertised as having an average return-on-equity (ROE)of 11.4 percent and a standard deviation of 3 percent.An inquiry is made by a prospective client who finds that the ROE is supposed to be normally distributed for these stocks.The prospective client obtains a list of the stocks and randomly samples 300 stocks and records the ROE.The results are: Re turn-on-Equity Category Observed Frequency Expected Frequency Under 6 14 9.93 6- under 10 92 85.83 10- under 14 146 146.58 14- under 18 46 53.49 18 or above 2 4.17 Total 300 300 -What is the calculated value of the chi-square test statistic?

In testing a population variance or constructing a confidence interval for the population variance,an essential assumption is that:

Biology A biology professor claimed that the proportions of grades in his classes are the same.A sample of 100 students showed the following frequencies: Grade F Frequency 18 20 28 23 11 -State the null and alternative hypotheses to be tested. H₀: ____________________________________________________________ H₁: ____________________________________________________________

Biology A biology professor claimed that the proportions of grades in his classes are the same.A sample of 100 students showed the following frequencies: Grade F Frequency 18 20 28 23 11 -Do the data provide enough evidence to support the professor's claim?

Of the values for a chi-squared test statistic listed below,which one is likely to lead to rejecting the null hypothesis in a goodness-of-fit test?

Department store A large department store records the number of returns per day in women's dresses for reasons such as wrong size; husband didn't like it,color,etc.The manager of the women's dresses department recalls from her statistics class in college that the Poisson distribution might describe such events.A random sample of 150 days is taken.The number of returns per day in the sample as well as the observed frequencies are shown below: Number of Returns Per Day Observed Frequency 0 21 1 37 2 44 3 30 4 14 >4 4 -She tests the hypothesis that returns per day are Poisson distributed with a population mean equal to 1.90.Her significance level is 0.05.Identify the critical value.

Gifts Three choices of free gifts are offered to 270 persons who subscribed to a new magazine.The number choosing each gift is shown in the table below.Assume the null hypothesis that the gifts are equally attractive to the subscribers.Use a 0.01 significance level. Gift Number Choosing gift A 110 B 100 C 60 -What is the conclusion?

Large city A large city is in the process of voting on a bond issue to build a covered sports arena.A local political analyst wishes to determine if the level of income will impact on the decision of the voters.He takes a sample of 350 who plan to vote in the upcoming election. Vote on Bond Issue Income Yes No Total Under \ 20,000 8 12 20 \ 20,000 - under \ 30,000 26 20 46 \ 30,000 - under \ 40,000 102 50 152 \ 40,000 - under \ 50,000 50 58 108 \ 50,000 or above 14 10 24 Total 200 150 350 -What is the expected frequency of the $50,000 and over and No categories?

What is the rationale for df = (r - 1)(k - 1)in conducting a chi-square test of independence for a contingency table with r rows and k columns?

Under the assumption that the null hypothesis is true,we construct a table of ____________________ that are based on the probability distribution from which the sample is assumed to have been drawn.

The null hypothesis states that the sample data came from a normally distributed population.The researcher calculates the sample mean and the sample standard deviation from the data.The data arrangement consisted of six categories.Using a 0.01 significance level,what is the appropriate critical value for this chi-square test?

The starting point for the chi-square test of variable independence is the ____________________.

By using chi-square analysis,we can compare two or more sample proportions at the same time.

Employee Four employees are monitored to determine whether there is any difference in the proportions of acceptable parts produced by the employees.The sample of parts produced is given below. Employee Quality Total Acceptable 265 270 225 180 950 Unacceptable 10 5 15 20 50 Total 275 275 250 200 1000 -These data provide the information for testing the hypothesis that the proportion of unacceptable is the same for the four employees.What will be the degrees of freedom for this test?

Hypotheses In testing the hypotheses: H₀: $\sigma ^ { 2 } = 0.01$ H₁: $σ ^ { 2 } \neq 0.01$ a random sample of 10 observations was drawn from a normal population,and the sample standard deviation was 0.043. -What is the conclusion?

The middle 0.95 portion of the chi-square distribution with 10 degrees of freedom has table values of: