Exam 13: Chi-Square Applications

In preparing a confidence level for a population variance,the size of the sample is 13,and the level of confidence is 0.90.What are the appropriate table values for this interval? ____________________ and ____________________

A researcher is studying cancer mortality rates for men in five southern states.In the five states,the sample standard deviation is 6.76 (per 100,000).A 98 percent confidence interval estimate of the population variance is represented by:

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 appropriate table value for the .10 significance level?

A sample of size 20 is used to obtain the following statistics: $\sum x _ { i } = 4363$ and $\Sigma \mathrm { x } _ { i } ^ { 2 } = 953,180$ Can we conclude at the 1% significance level that the population variance is less than 100? Hypotheses: Test statistic = ____________________ Critical Value = ____________________ Conclusion: _________________________ Interpretation: __________________________________________________

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 expected frequency of the Hotel or Motel category?

A random sample of 5 observations was drawn from a normal population.These were: 18,16,10,13,and 23.Estimate the population variance with 90% confidence. Lower value = ____________________ Upper value = ____________________

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 -Compute the value of the test statistics.

In order to use the chi-square distribution to construct confidence intervals and carry out hypothesis tests regarding the value of a population variance,an important assumption to be made is that the population is chi-square distributed.

To use the chi-square distribution table to select a table value requires the following:

Survey In a survey of 100 males and 100 females at a regional university,26 percent of the males and 18 percent of the females responded that they were offended by frequently aired television.The test question is: Could these results indicate that the same proportions of the two samples are offended? -What is the calculated value of the test statistic?

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.What are the appropriate degrees of freedom?

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 -Employing a 0.10 significance level,what is the appropriate conclusion based on the calculations from the above data?

Like the critical values for the normal distribution and the t-distribution,the critical values for the chi-square distribution can be either positive or negative.

Video The owner of a video store is interested in whether or not there is a difference in the proportions of VCR movies rented by members and non-members among movie titles.Three movies are selected and each person who rents them is identified as a member or non-member.A total of 350 people rent these movies and the responses are: Mo vie Membershị Witness Rambo Karate Kid Total Member 21 14 70 105 Non-Member 79 86 80 245 |Total 100 100 150 350 -What is the critical value for a 0.01 significance level?

Although the chi-square distribution is continuous,it is used to analyze discrete (counts)data.

A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

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 are the appropriate degrees of freedom based on the above data?

Survey In a survey of 100 males and 100 females at a regional university,26 percent of the males and 18 percent of the females responded that they were offended by frequently aired television.The test question is: Could these results indicate that the same proportions of the two samples are offended? -What are the observed frequencies of the males and females who are offended by the ads? Males: ____________________ Females: ____________________

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 conclusion?

The Forest Management Institute is conducting a test,which involves measuring the size of trees by photographing from helicopter rather than actual field measurement.This process is especially important in forest areas accessible only by helicopter.A sample of 31 trees measured by aerial photography had a sample standard deviation of 2.24.A 95 percent confidence interval for the population variance is represented by the values: