Question

1) Suppose a person claims that the proportion of all adults living in San Bernardino County that are left-handed is less than 20%. A researcher decides to test this claim. Fill in the blanks and indicate which hypothesis is the claim in this case a) The null hypothesis Ho is: b) The alternative hypothesis H, is: c) Is this a two-tailed, right-tailed, or left-tailed test? The researcher decides to use a significance level of 0.05 for this test. Now suppose that the researcher collects a random sample of 250 adults living in San Bernardino County and 45 of them are left-handed. d) Draw a good diagram for the distribution of the standardized test statistic showing the location of the critical value(s) and the rejection region. What is (are) the critical value(s) for this test? e) What is the observed value of the standardized test statistic? Show some work including the formula for the test statistic ) Write a good conclusion for this test. Should we accept or reject the claim? Conclusion:

Answer 1

Here we have x=45, n=250, p=0.18 Hypotheses are Ho: p= 0.2 H p 0.2 Level of significance: α=0.05 Test is left tailed The standard deviation is: Pl-p) sqrt((0.2*(1-0.2))/250) n 0.0253 Test Statistics p-p =(0.1892)/(0.0253) --0.79 Critical value: CV --1.645 Rejection Region: If z <-1.645, Reject HO Decision: Since test statistics does not lie in rejection region so we fail to reject the null P-value: P-value-0.2148 Decision: Since p-value is not less than level of significance so we fail to reject the null Excel function for critical value: NORMSINV(0.05) Excel function for p-value: NORMSDIST(-0.79)

Following is the graph showing critical value:

2 2 3

f)

We fail to reject the null hypothesis. We cannot conclude that proportion of left handed people in the county is less than 20%.