Exam 10: Chi-Square Tests and the F-Distribution

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value. Calculate the test statistic. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A researcher wants to determine whether the time spent online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Gender Time spent online per day (minutes) 0-30 30-60 60-90 90+ Male 25 35 75 45 Female 30 45 45 15 Test the hypothesis that the time spent online per day is related to gender. Use $\alpha = 0.05$

Perform the indicated one-way ANOVA test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic F. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that each population is normally distributed and that the population variances are equal. -Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Test the claim that the type of fertilizer makes no difference in the mean number of raspberries per plant. Use $\alpha = 0.01$ 5 Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4 6 5 6 3 5 8 3 5 7 5 4 3 6 5 2 4 7 5 3 4 6 6 3 5 3 3 4 4 5

Find the marginal frequencies for the given contingency table -The following contingency table was based on a random sample of drivers and classifies drivers by age group and number of accidents in the past three years. Number of Age accidents <25 25-45 >45 0 96 145 287 1 20 67 62 >1 20 8 26

The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Find the critical value χ $\chi _ { 0 } ^ { 2 }$ , to test the claim of independence using α = 0.05.

A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Find The test statistic F to test the claim that there is no difference in the average age of each group. Elementary Teachers High School Teachers Community College Teachers 23 36 45 28 38 45 27 41 36 52 47 61 25 42 39 37 31 35

Find the critical $\mathrm { F } _ { 0 }$ -value to test the claim that the populations have the same mean. Use $\alpha = 0.05 \text {. }$ Brand 1 Brand 2 Brand 3 =8 =8 =8 =3.0 =2.6 =2.6 =0.50 =0.60 =0.55

Find the left-tailed and right-tailed critical F-values for a two-tailed test. Let α $\alpha$ = 0.02, d.f.N = 7, and d.f.D = 5.

Find the critical value $F _ { 0 }$ to test the claim that $\sigma _ { 1 } ^ { 2 } > \sigma _{ 2 }^ { 2 }$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $\alpha = 0.01 .$ =16 =13 =1600 =625

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are independent and that each population has a normal distribution. -A local bank has the reputation of having a variance in waiting times as low as that of any bank in the area. A competitor bank in the area checks the waiting time at both banks and claims that its variance of waiting times is lower than at the local bank. The sample statistics are listed below. Test the competitorʹs claim. Use $\alpha = 0.05 \text {. }$ Local Bank Competitor Bank =41 =61 =2 minutes =1.1 minutes

The weights of a random sample of 25 women between the ages of 25 and 34 had a standard deviation of 28 pounds. The weights of a random sample of 41 women between the ages of 55 and 64 had a standard deviation of 21 pounds. Construct a 95% confidence interval for $\frac { \sigma _ { 1 } ^ { 2 } } { \sigma _ { 2 } ^ { 2 } } , \text { where } \sigma _ { 1 } ^ { 2 } \text { and } \sigma _ { 2 } ^ { 2 }$ are the variances of the weights of women between the ages 25 and 34 and the weights of women between the ages of 55 and 64 respectively.

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value. Calculate the test statistic. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. -The contingency table below shows the party and opinions on a bill of a random sample of 200 state representatives. Party Opinion Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Test the claim that opinions on the bill are dependent on party affiliation. Use α $\alpha$ = 0.05 .

A new coffeehouse wishes to see whether customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Test the claim that the distribution is uniform. Use $\alpha$ = 0.01. Brand 1 2 3 4 5 Customers 55 32 30 65 18

A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Find The critical value F0 to test the claim that there is no difference in the average age of each group. Use $\alpha$ = 0.01. Elementary Teachers High School Teachers Community College Teachers 23 41 39 28 38 45 27 36 36 37 47 61 25 42 45 52 31 35

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are independent and that each population has a normal distribution. -A local bank has the reputation of having a variance in waiting times as low as that of any bank in the area. A competitor bank in the area checks the waiting time at both banks and claims that its variance of waiting times is lower than at the local bank. The sample statistics are listed below. Test the competitorʹs claim. Use $\alpha = 0.05$ \begin{array}{llcc} \text { Local Bank } & \text {Competitor Bank } \\ \text { \mathrm{n}_{1}=13 } & \text { \(\mathrm{n}_{2}=16\)} \\\\ \text { \(s _1=1.69 \text {minutes}\) } & \text { \(s_2=1.43\text { minutes }\) } \\\end{array}

The frequency distribution shows the ages for a sample of 100 employees. Find the expected frequencies for each class to determine if the employee ages are normally distributed. Class boundaries Frequency, f 29.5-39.5 14 39.5-49.5 29 49.5-59.5 31 59.5-69.5 18 69.5-79.5 8

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value. Calculate the test statistic. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A sports researcher is interested in determining if there is a relationship between the type of sport and type of team winning (home team versus visiting team). A random sample of 526 games is selected and the results are given below. Football Basketball Soccer Baseball Home team wins 39 156 25 83 Visiting team wins 31 98 19 75 Test the claim that the type of team winning is independent of the type of sport. Use $\alpha = 0.01$

A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Calculate the chi-square test statistic χ $\chi ^ { 2 }$ to test the claim that the Distribution is uniform.. Brand 1 2 3 4 5 Customers 30 65 18 32 55

Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on Until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting Positions. Find the critical value χ $\chi _ { 0 } ^ { 2 }$ to test the claim that the number of wins is uniformly distributed across The different starting positions. The results are based on 240 wins. Starting Position 1 2 3 4 5 6 Number of Wins 32 50 44 33 36 45

Perform the indicated one-way ANOVA test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic F. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that each population is normally distributed and that the population variances are equal. -A researcher wishes to compare times it takes workers to assemble a certain computer component using different machines. Workers are randomly selected and randomly assigned to one of three different machines. The time (in minutes)it takes each worker to assemble the component is recorded. Test the claim that there is no difference in the mean assembly times for the three machines. Use $\alpha = 0.01$ Machine 1 Machine 2 Machine 3 32 40 31 32 29 28 31 38 29 30 33 25 33 36 31 32 35

Perform the indicated one-way ANOVA test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic F. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that each population is normally distributed and that the population variances are equal. -The grade point averages of students participating in sports at a local college are to be compared. The data are listed below. Test the claim that at least one group has a different mean. Use $\alpha = 0.05$ Tennis Golf Swimming 2.6 1.8 2.7 3.2 3.3 2.5 2.5 1.9 2.8 3.5 2.1 3.0 3.1 2.5 2.1