Hypothesis Tests for a Population Mean

1. Some sources report that the weights of full-term newborn babies have a mean of 6.5 pounds. A pediatrician believes that the average weight of full-term newborn baby is slightly increased. A random sample of 30 full-term newborn baby is selected with an average weight of 7 pounds and a standard deviation of 0.8 pounds. Conduct the hypothesis test at 5% significance level.

2. A fast-food chain claims that their "HUGE" size drink contains 36.3 ounces on average. A customer wants to test that the "HUGE" size drink contains less amount of drink. A random sample of 50 "HUGE" size cups is taken. The average weight of the drink from the sample is 35.8 ounces with a standard deviation of 0.78 ounces. Conduct the hypothesis test at 10% significance level.

3. In 1960, census results indicated that the age at which American mean first married had a mean of 25.3 years. It is widely suspected that young people today have different opinion about when to get married. A random sample of 32 young men is taken. The average married age of the sample is 28.6 with a standard deviation of 5.4. State the hypothesis testing that people nowadays get married at a different average age of 25.3 years-old. Use 1% significance level.