19A. According to the state's COVID website as of 4/29/21, 30.9% of Allegany County residents have had at least one vaccine dose. The leaders of Independence wish to know if their rate is lower than the county. In a random sample of 32 Independence residents out of the 1,167 residents, 9 had at least one vaccine dose. At the 2% level, can the leaders of Independence state their rate is lower than the county rate? Provide proof using the four steps of the hypothesis test, if necessary

19B. According to a website as of 2016, the average weight of US males who are 20 or older is 197.1 pounds. A researcher wishes to know if the current average weight of US males who are 20 or older is different. In a random sample of 254 US males who are 20 or older, the mean weight was 214. 6 pounds and the standard deviation was 45.86 pounds. At the 2% level, can the researcher state the mean weight has changed? Provide proof using the four steps of the hypothesis test, if necessary