Question

Suppose it is reported 23% of Ball State students are out of state. You take a sample of 50 Ball State students and find that 9 of them are out-of-state students, such that LaTeX: \hat{p}=.18 p ^ = .18 . If you want to test for whether or not the percent of Ball State students is less than the reported 23%, which of the following is the null and alternative hypotheses for this test? LaTeX: H_0 \colon p=.18 ; H_A \colon p\ne .18 H 0 : p = .18 ; H A : p ≠ .18 H 0 : p = .18 ; H A : p ≠ .18 H 0 : p = .18 ; H A : p ≠ .18 LaTeX: H_0 \colon \le p=.18 ; H_A \colon p> .18 H 0 : ≤ p = .18 ; H A : p > .18 H 0 : ≤ p = .18 ; H A : p > .18 H 0 : ≤ p = .18 ; H A : p > .18 LaTeX: H_0 \colon \ge p=.18 ; H_A \colon p < .18 H 0 : ≥ p = .18 ; H A : p < .18 H 0 : ≥ p = .18 ; H A : p < .18 H 0 : ≥ p = .18 ; H A : p < .18 LaTeX: H_0 \colon \ge p=.23 ; H_A \colon p< .23 H 0 : ≥ p = .23 ; H A : p < .23 H 0 : ≥ p = .23 ; H A : p < .23 H 0 : ≥ p = .23 ; H A : p < .23 Flag this Question Question 2 1 pts What is the test statistic for the above hypothesis test? -22.10 -0.84 -0.92 16.94 Flag this Question Question 3 1 pts Assume, that the hypothesis you want to test is the following: LaTeX: H_0 \colon p=.23 ; H_A \colon p\ne .23 H 0 : p = .23 ; H A : p ≠ .23 What are the critical values for conducting the hypothesis test in question 5, at the 10%, 5%, and 1% levels? ±1.282, ±1.645, ±2.326 ±1.645, ±1.960, ±2.576 -1.299, -1.677, -2.405 -1.282, -1.645, -2.326 Flag this Question Question 4 1 pts Assume you found the test statistic of the above hypothesis test to be -1.83, at what significance levels could you reject the following null hypothesis: LaTeX: H_0 \colon p=.23 ; H_A \colon p\ne .23 H 0 : p = .23 ; H A : p ≠ .23 Just the 10% level The 5% and 1% levels The 10%, 5%, and 1% levels The 10% and 5% levels

Answer 1

GIVEN:

Sample size

Number of students who are out of state

HYPOTHESIS:

(That is, the proportion of students who are out of state is not significantly different from %.)

(That is, the proportion of students who are out of state is significantly different from %.)

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows standard normal distribution.

where is the hypothesized value .

CALCULATION:

The sample proportion is,

  

Now

  

  

CRITICAL VALUES:

The two tailed z critical value at significance level is .

The two tailed z critical value at significance level is .

The two tailed z critical value at significance level is .

DECISION RULE:

CONCLUSION:

Since the calculated z test statistic (-0.84) is greater than the z critical value (-1,960,-2.576,-1.645), we fail to reject null hypothesis and conclude that the proportion of students who are out of state is not significantly different from % at 5%,1% and 10% level of significance.