Question

2. A researcher posted that based on a random sample they did not find statistically significant evidence that the proportion of people following appropriate distancing and mask guidelines was different than 0.50.

a. State the null and alternative hypotheses.

b. How many sides does this test have?

c. Briefly explain what the researcher meant by “they did not find statistically significant evidence”.

3. To test the claim that the percentage of voters that voted in the last presidential election is less than 60%, a researcher randomly sampled 900 voters. 513 voted in the last election.

a. State the null and alternative hypotheses.

b. Compute the test statistic (z value).

c. Compute the P-value.

d. What conclusion should be made at a 5% significance level?

Answer 1

• Here, we are to test if the proportion is "different" from 0.50. Thus, the Null is "not different" from 0.5 and the Alternative is "different from" 0.5. That is, the null hypothesis is given by:
  
  
• The test has two sides - the lesser than value and the greater than value.
  
• "They didnot find statistically significanct evidence" means that the sample does not produce enough evidence to do away with the Null and accept the alternative claim. That is, the value of the test statistic is in the acceptance region of the Null.
  
• Here, we are to test if the proportion is less than 0.60. That is, we are to test:
  
  
• The test statistic is given by:
  
  The values are given as:
  
  
  
  
  Hence,
  
  
• Under Null,
  
  
  The p-value is given by:
  
  
  
  
  
• We reject at 5% level of significance if the p-value is less than 0.05.
  
  It is observed that the p-value is less than 0.033. Hence we reject the Null hypothesis and claim that the proportion is less than 0.6.
  

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