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Sun. Mon. Tues. Wed. Thurs. Fri. Sat. For each of these questions: A) State the hypotheses and identify which hypothesis represents the claim. B) Find the standardized test statistic C) Find the p-value D) Make a decision regarding the claim. 1) A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table shows the day of the week for which 782 randomly selected fatal bicycle accidents occurred. At 𝛼=0.10, can you reject the claim that the distribution is uniform? The contingency table shows the educational attainment of a random sample of adults in the United States by age in a recent year. Conduct a test for independence, using α = 0.10. Assume that the variables are independent. Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 108 112 105 111 123 118 H.S. – did not complete H.S. completed College 1-3 years 4 or more years 25-44 556 1359 1217 1347 45 and older 964 1941 1389 1488

L1 holds the claimed percentages 1) A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table shows the day of the week for which 782 randomly selected fatal bicycle accidents occurred. At 𝛼=0.10, can you reject the claim that the distribution is uniform? Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 108 112 105 111 123 118 SOLUTION: 𝐻 0 : The distribution of fatal bicycle deaths by day of the week is uniform. 𝐻 𝑎 : The distribution of fatal bicycle deaths by day of the week is not uniform. STAT - Edit L1 holds the claimed percentages Since the claim is that the distribution is uniform, ALL the percentages will be equal to each other. There are 7 categories, so divide 1 by 7 to get the claimed percentage. Type “1/7” into L1 7 times (one for each category).

L2 holds the observed frequencies 1) A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table shows the day of the week for which 782 randomly selected fatal bicycle accidents occurred. At 𝛼=0.10, can you reject the claim that the distribution is uniform? Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 108 112 105 111 123 118 SOLUTION: 𝐻 0 : The distribution of fatal bicycle deaths by day of the week is uniform. 𝐻 𝑎 : The distribution of fatal bicycle deaths by day of the week is not uniform. STAT - Edit L2 holds the observed frequencies Enter the numbers shown in the table into L2 L3 holds the expected values Highlight L3 and type "L1*782", since n = 782. L3 should have 111.714 in all 7 rows.

Observed is in L2, Expected is in L3, 1) A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table shows the day of the week for which 782 randomly selected fatal bicycle accidents occurred. At 𝛼=0.10, can you reject the claim that the distribution is uniform? Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 108 112 105 111 123 118 SOLUTION: STAT - TEST - D Observed is in L2, Expected is in L3, Degrees of Freedom (df) = 6 (k – 1, where k is the number of categories) 𝑋 2 =2.43 (Standardized test statistic) 𝑝=.876 Since 𝑝>𝛼, we fail to reject the null. This means that at the 10% significance level, there is not enough evidence to reject the claim that the distribution of fatal bicycle accidents throughout the week is uniform.

𝐻 𝑎 : The variables years of education attained and age are dependent. The contingency table shows the educational attainment of a random sample of adults in the United States by age in a recent year. Conduct a test for independence, using α = 0.10. Assume that the variables are independent. A) 𝐻 0 : The variables years of education attained and age are independent. 𝐻 𝑎 : The variables years of education attained and age are dependent. The null hypothesis is the claim. 2nd Matrix, Edit 1 (A) Create a 2 x 4 matrix and enter the numbers from the table into that matrix. Stat-Test-C Matrix A is the Observed Matrix B is the Expected. Access Matrix B (2nd Matrix Edit 2) and confirm that all cell values are > 5. H.S. – did not complete H.S. completed College 1-3 years 4 or more years 25-44 556 1359 1217 1347 45 and older 964 1941 1389 1488

The standardized test statistic is 𝛸 2 = 66.182 The contingency table shows the educational attainment of a random sample of adults in the United States by age in a recent year. Conduct a test for independence, using α = 0.10. Assume that the variables are independent. The standardized test statistic is 𝛸 2 = 66.182 C) The p-value is 2.877E-14 D) Since p < α, we reject the null. Since the null is the claim, we also reject the claim. This means that the variables are dependent, or related to each other. H.S. – did not complete H.S. completed College 1-3 years 4 or more years 25-44 556 1359 1217 1347 45 and older 964 1941 1389 1488