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A confidence interval for the population mean ?� tells us which values of ?� are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence. You can use this idea to carry out a test of any null hypothesis ?0:?=?0�0:�=�0 starting with a confidence interval: reject ?0�0 if ?0�0 is outside the interval and fail to reject if ?0�0 is inside the interval.
The alternative hypothesis is always two‑sided, ??:?≠?0��:�≠�0 because the confidence interval extends in both directions from ?⎯⎯⎯.�¯. A 95% confidence interval leads to a test at the 5% significance level because the interval is wrong 5% of the time. In general, confidence level ?� leads to a test at significance level ?=1−?.l
A medical director found the LDL cholesterol ?⎯⎯⎯=124.86�¯= for an SRS of 72 executives. The standard deviation of the LDL of all adults is ?=40.is .
Give a 90% confidence interval for the mean LDL ?� of all executives in this company, assuming that the standard deviation is the same as for all adults.
Give your answer as an interval in the form (*, *). Give your numbers to two decimal places.
The hypothesized value ?0=130 falls inside this confidence interval. Carry out the ?� test for ?0:?=130�0 against the two‑sided alternative.
Find the test statistic ?.�. Give your answer to two decimal places.
Find the ?-value�-value for the ?� test. Give your answer to four decimal places.
The hypothesized value ?0=134 falls outside this confidence interval. Carry out the ?� test for ?0:?=134�against the two‑sided alternative.
Find the test statistic ?.�. Give your answer to two decimal places.
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