Question

ule 1.15, 1.15, 1.01, 1.03 1.15. 1.22. 1.03, 1.13, 1.21, an cat orde 1.35 (a) Given that X-1.14 and s 0.10 for these ten years, use t at the :01 tevet of signit cance to test the null hypothesis that the temperature of earth is not getting warmer In other words, could the sample mean deviation for these ten years have originaterd from a population of annual deviations for the entire twentieth century having a mean deviation equal to zero? (b) If appropriate (because the null hypothesis has been rejected), construct a 99 per- cent confidence interval and interpret this interval. Answers on page 437. 13.8/Assume that, on average, healthy young adults dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean, X, of 88 minutes and a sample standard deviation, s, of 9 minutes. (a) Use tto test the null hypothesis at the .05 level of significance. (b) If appropriate (because the null hypothesis has been rejected), construct a 95 per 13.9 In the gas mileage test described in this chapter, would you prefer a smaller or a (a) the car manufacturer? Why? (b) a vigorous prosecutor for the federal regulatory agency? Why? cent confidence interval and interpret this interval. larger sample size if you were rather than the more appropriate t to test a hypothesis at the .05 level of signifi- cance. 13.10 Even though the population standard deviation is unknown, an investigator uses (a) Is the true level of significance larger or smaller than 05? (b) Is the true critical value larger or smaller than that for the critical 2?

Answer 1

For unknown sigma and n <30 we use 1sample t test.

t= x-u/(s/sqrt (n))

And the confidence interval is x +- t (s/sqrt (n))