Question

1. Follow the procedure for Testing a hypothesis:

A county is interested in finding the proportion of the population that Hs been vaccinated for the  flu this season.  A Simple random sample of 680 residents is taken and it is found that 357 have been vaccinated.  Claim: Over 50% of the population has been vaccinated for the blue with a level of significance or 0.01.

Step 2:  Determine Ho and Ha. Express Ho and Ha both verbally and symbolically.  The symbolic representation includes the parameter that is being tested.  

Step 3:  Determine the distribution for the test.  Identify the test statistic – give the actual formula!  Determine if the test is right tailed, left tailed or two tailed.

Step 4:  Check to see assumptions for the test are met.  Identify the level of significance of the test – pick a.

Step 5:   Draw a graph, calculate the test statistic, and use the test statistic to calculate the p-value. (A z-score and a t-score are examples of test statistics.).  Show calculations.

Step 6:  Compare the preconceived awith the p-value, decide whether the data supports rejecting Ho or failing to reject Ho.

Step 7:  Write a clear conclusion in the context of the original hypothesis using English sentences.

Answer 1

Step 2: Null hypothesis: H: p 0.50 That is, 50% of the population has been vaccinated for the blue Alternative hypothesis: Ha:p>0.50 That is. Over 50% of the population has been vaccinated for the blue Step 3:

72 0.525-0.50 0.50 (1-0.50) 680 0.025 0.0192 The value oftest statistic is z1.30 This test is right tailed. Step 4: Assumptions: The sample must be reasonably randonm The sample must be less than 10% of the population The sample must be large enough so that np and np(1-p)210

Step 5: P-Value-0.0968 .2 0 test z-1.3 The p-value is 0.0968 Step 6: Use a significance level, α-001 Here, p-value is 0.0968, which is greater than the value of α That is, p-value(-0.0968)> α(-0.01) 0.01

Therefore, by the rejection rule, do not reject the null hypothesis Ho Step 7: Conclusion: There is insufficient evidence at level of significance α-001 That is, 50% of the population has been vaccinated for the blue