In a clinical study of an allergy drug, 108 of the 203 subjects reported experiencing significant relief from their symptoms. Using a significance level of .01, test the claim that more than half of all those using the drug experienced relief.

-According to a recent poll, 53% of Americans would vote for an incumbent president. If a sample of 100 people results in 45% who would vote for the incumbent, test the claim that the percentage is 53%. Use a .10 significance level.

- A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus 14 during peak hours on 18 different occasions. Her mean waiting time was 7.4 minutes. Assume that the standard deviation has been historically known to be 2.2 minutes. At the .05 significance level, test the claim that the mean waiting time is less than 10 minutes.

-The world's smallest mammal is the bumblebee bat. Such bats are roughly the same size of a large bumblebee. Listed below are the weights (in grams) from a sample of these bats. Assuming that all such bats have a standard deviation of .3 grams, use a significance level of .05 to test the claim that these bats are from the same population with a known mean of 1.8 grams. Do the bats appear to be from the same population ? You may assume the sample data comes from a population that follows a normal distribution. 2.13 1.31 1.91 1.92 1.77 1.64 2.29 1.99 2.33 2.49 2.22

-A manufacturer makes steel rods that are supposed to have a mean length of 50 centimeters. A retailer suspects that the bars are being produced too short. A sample of 46 bars is taken and their mean length is determined to be 51 centimeters with a standard deviation of 3.6 centimeters. Using a .01 significance level, test the retailers claim that the population mean is less than 50 centimeters.

what is the null hypothesis, alternative hypothesis, significance/alpha level, p-value for these questions?