The men body mas index (BMI) for boys of age 12 years is 23.6kg/m An investigator wants to test if the BMI is higher in 12-year-old boys living in New York CIty. How many bos are needed to ensure that a two-sided test of hypothesis has 80% power to detect a difference in BMI of 2 kg/m? Assume that the standard deviation in BMI is 5.7 kg/m.

a random sample of 22 diamonds from a jewerly dealer gives an average weight of 0.86 carats with a standard deviation of 0.42 carats. Test whether the mean weight is less that 1 carat at the 0.01 level

The average healing time of a certain type of incision is 288 ​hours, with a standard deviation of 30 hours. What percentage of the people having this incision would heal in 9 days or​ less? Assume a normal distribution.

A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 9 years. A survey of 69 companies reported in The Wall Street Journal found a sample mean tenure of 8.8 years for CEOs with a standard deviation of s=s= 4 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed.You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of α=0.10α=0.10. Your hypotheses are:      Ho:μ=9Ho:μ=9      Ha:μ<9Ha:μ<9What is the test statistic for this sample?test statistic =  (Report answer accurate to 3 decimal places.) What is the p-value for this sample?p-value =  (Report answer accurate to 4 decimal places.)  The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to...…