Question

The table below shows the frequency with which samples of people from New York and people from California characterized their level of worry about getting Covid19. Do not do the entire hypothesis test, but in the space below, write the 1)null and alternative, 2)the critical value (using alpha=.05), and only 3) the expected frequency for very worried in California.

	not worried	slightly worried	very worried
New York	20	60	80
California	80	100	50

Answer 1

Chi-Square Independence test - Results

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - Level of worry and State are independent Ha​: The two variables - Level of worry and State are dependent This corresponds to a Chi-Square test of independence. (2) Critical value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2, so the critical value is 5.9915. Then the rejection region for this test becomes R={χ2:χ2>5.9915}. (3) the expected frequency for very worried in California = 76.6667 Additional information: Test Statistics The Chi-Squared statistic is computed as follows: P-value The corresponding p-value for the test is p=Pr(χ2​>41.7024)=0 The decision about the null hypothesis Since it is observed that χ2=41.7024>χ2_c​rit=5.9915, it is then concluded that the null hypothesis is rejected. Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables - Level of worry and State are dependent, at the 0.05 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.

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