Question

(Survey from 9.41: In a survey of 446 students, it was found that 50% of the sampled students lived on campus and 50% lived off campus.)

In the same survey used in 9.41, 88% of the sampled students were right-handed.

a. The proportion of all people who are right-handed is said to be 0.88. Tell the value of standardized sample proportion z, if we want to test whether the proportion of all students who are right- handed could be 0.88.

b. If we sketch a normal curve for the distribution of sample proportion (centered at 0.88), what portion should be shaded to indicate the area represented by the P-value for testing against the alternative that population proportion is less than 0.88? [Please see the three graphs on p. 000 for examples of P-value as a shaded area.]

c. What portion of the standard normal (z) curve should be shaded to indicate the area represented by the P-value for testing against the alternative that the population proportion is less than 0.88? What does the P-value equal in this case?

d. What portion of the normal curve for the distribution of sample proportion (again, centered at 0.88) should be shaded to indicate the area represented by the P-value for testing against the (two-sided) alternative that population proportion does not equal 0.88? What does the P-value equal in this case?

e. What portion of the normal curve for the distribution of standardized sample proportion z should be shaded to indicate the area represented by the P-value for testing against the (two-sided) alternative that population proportion does not equal 0.88?

f. Will the null hypothesis be rejected against either the one-sided or two-sided alternative? Explain.

Answer 1

a. Since the sample value is .88 and we wish to test whether population proportion is .88, z value will be 0.

b. The asymptotic distribution of sample proportion is N(.88,SD=sqrt(.88*.12/446)=0.01538737)

The plot gives the shaded region (the left of the vertical line at .88) as the desired .

c. The plot gives the shaded region (the left of the vertical line at .0) as the desired .. Due to symmetry of normal curve, the area is 0.5 and hence p value is 0.5

d. The plot gives the shaded region (all the area to the left and the right of the vertical line at .88) as the desired . Since all the region is covered under the normal curve, area is unity and hence p value is unity.

e.The plot gives the shaded region (all the area to the left and the right of the vertical line at 0) as the desired .

f. The evidence is not sufficient against the null as p value is .5 in the one sided case and unity in the two sided case. Hence we fail to reject the null.

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