Question

Is achieving a basic skill level related to the location of the​ school? The results of a random sample of students by the location of school and the number of students achieving basic skill levels in three subjects is shown in the contingency table. At alpha equals 0.01 α=0.01​, test the hypothesis that the variables are independent. Complete parts​ (a) through​ (d). Subject Location Reading Math Science Urban 43 43 50 50 43 43 Suburban Suburban 70 70 69 69 59 59 ​(a) Identify the claim and state the null and alternative hypotheses. Upper H 0 H0​: Skill level in a subject is ▼ dependent on independent of location. Upper H Subscript a Ha​: Skill level in a subject is ▼ independent of dependent on location. The ▼ null hypothesis alternative hypothesis is the claim. ​(b) Determine the degrees of​ freedom, find the critical​ value, and identify the rejection region. What are the degrees of​ freedom? d.f. equals = nothing Find the critical value. chi Subscript 0 Superscript 2 χ20 equals = nothing ​(Round to three decimal places as​ needed.) Choose the correct rejection region below. A. chi squared χ2 greater than > chi Subscript 0 Superscript 2 χ20 B. chi squared χ2 less than < chi Subscript 0 Superscript 2 χ20 C. chi squared χ2 greater than or equals ≥ chi Subscript 0 Superscript 2 χ20 D. chi squared χ2 less than or equals ≤ chi Subscript 0 Superscript 2 χ20 ​(c) Calculate the test statistic. If​ convenient, use technology. chi squared χ2 equals = nothing ​(Round to three decimal places as​ needed.) ​(d) Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. Choose the correct conclusion below. A. Fail to reject Fail to reject the null hypothesis. There is not is not enough evidence to reject the claim that skill level in a subject is independent of location. B. Reject Reject the null hypothesis. There is is enough evidence to reject the claim that skill level in a subject is independent of location. C. Reject Reject the null hypothesis. There is not is not enough evidence to reject the claim that skill level in a subject is independent of location. D. Fail to reject Fail to reject the null hypothesis. There is is enough evidence to reject the claim that skill level in a subject is  independent of location.

Answer 1