1) The null hypothesis, H_o: = 43, was tested against the alternative hypothesis, H_a: > 43. A sample of 79 resulted in a calculated p-value of 0.074. If = 3.3, find the value of the sample mean, x. (Give your answer correct to one decimal place.)

2) The null hypothesis, H_o: = 15.5, was tested against the alternative hypothesis, H_a: < 15.5. A sample of 45 resulted in a calculated p-value of 0.017. If x = 13.5, find the value of the population standard deviation. (Give your answer correct to two decimal places.)

3)The owner of a local chain of grocery stores is always trying to minimize the time it takes her customers to check out. In the past, she has conducted many studies of the checkout times, and they have displayed a normal distribution with a mean time of 12.7 minutes. and a standard deviation of 2.4 minutes. She has implemented a new schedule for cashiers in hopes of reducing the mean checkout time. A random sample of 35 customers visiting her store this week resulted in a mean of 11.3 minutes. Does she have sufficient evidence to claim the mean checkout time this week was less than 12.7 minutes? Use = 0.02.(a) Find z. (Round your answer to two decimal places.) (ii) Find the p-value. (Round your answer to four decimal places.)

4) Consider the following. (Round your answers to four decimal places.)

(a) Calculate thep-value forH₀:= 20,H_a:< 20;x=17.7,=9.3,n=28. (b) Calculate thep-value forH₀:= 78.5,H_a:> 78.5;x=81.4,=15.8,n=36. (c) Calculate thep-value forH₀:= 1.587,H_a:1.587;x=1.615,=0.17,n=37.