Suppose that only 40% of the U.S. public supported the general direction of the previous U.S. administration's policies. To gauge whether the nationwide proportion, p, of support for the current administration is higher than 40%, a major polling organization conducts a random poll to test the hypotheses:

H_o: p = .40

H_a: p > .40

The results are reported to be not statistically significant, with a p-value of .214.

Decide whether each of the following statements is a valid conclusion or an invalid conclusion, based on the study:

1. The results do not reject the null hypothesis:
   • valid
   • invalid
   
   
   
2. The results provide enough evidence to accept the null hypothesis:
   • valid
   • invalid
   
   
   
3. The results indicate that it must be true that the nationwide proportion, p, of support for the current administration is equal to 40%:
   • valid
   • invalid
   
   
   
4. The results indicate that the nationwide proportion, p, of support for the current administration might be greater than 40%, but the sample size in the study might have been too small to detect a statistically significant difference:
   • valid
   • invalid