a) Assume that a sample is used to estimate the mean tip earned by a serving staff at a diner. Find the margin of error

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a)
Assume that a sample is used to estimate the mean tip earned bya serving staff at a diner. Find the margin oferror M.E. that corresponds to a sample of size14 servers with a mean of $83.38 and a standard deviation of $5.21at a confidence level of 97%.
Report ME accurate to one decimal place because the samplestatistics are presented with this accuracy.
M.E. = $
b) The effectiveness of a blood-pressure drug is beinginvestigated. An experimenter finds that, on average, the reductionin systolic blood pressure is 33.3 for a sample of size 504 andstandard deviation 14.6.Estimate how much the drug will lower a typical patient's systolicblood pressure (using a 99% confidence level).Enter your answer as a tri-linear inequality accurate to onedecimal place (because the sample statistics are reported accurateto one decimal place).
c)
If n=28, ¯x=36x¯=36, and s=7, find the margin of error at a80% confidence levelGive your answer to two decimal places.
d) In a survey, 17 people were asked how much they spent ontheir child's last birthday gift. The results were roughlybell-shaped with a mean of $31 and standard deviation of $5. Findthe margin of error at a 80% confidence level.Give your answer to two decimal places.
e) If n=26, ¯xx¯(x-bar)=41, and s=15, construct aconfidence interval at a 95% confidence level. Assume the data camefrom a normally distributed population.Give your answers to one decimal place. f) You intend to estimate a population mean with aconfidence interval. You believe the population to have a normaldistribution. Your sample size is 27.Find the critical value that corresponds to a confidence level of99.9%.(Report answer accurate to three decimal places withappropriate rounding.)