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Examples - inferences for one mean

# Examples - inferences for one mean - 3 The heights of...

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Examples 1 1. The heights of female university students are approximately normally distributed with a standard deviation 6 cm. A sample of 9 female university students yields a mean height of 177 cm. (a) Find a 95% confidence interval for the mean height of all female university students. (b) Interpret the 95% confidence interval in part (a). (c) Find a 90% confidence interval. (d) Find the sample size required to have a margin of error of 0.5 cm and a 95% confidence level. 1 Courtesy of Dr. Nosal

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2. Test of hypothesis for one population mean (when σ is known) It is known from studies performed in the past that the weight of Fraser River sockeye salmon during each annual run follows a normal distribution with a standard deviation of 0.5 lb. However the mean weight of fish may fluctuate from year to year depending on many ecological and genetic factors. A researcher would like to test whether or not this year’s run has a mean population weight of 5 lb. A random sample of nine fish yielded a mean of 4.7 lb. Test the hypothesis of the researcher at the 5% significance level.

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Unformatted text preview: 3. The heights of female university students are approximately normally. A sample of 9 female university students yields a mean height of 177 cm and a standard deviation of 6 cm. (a) Find a 95% confidence interval for the mean height of all female university students. (b) Find a 90% confidence interval. (c) Interpret the 90% confidence interval in part (b). 4. Test of hypothesis for one population mean (when σ is unknown) It is known from studies performed in the past that the weight of Fraser River sockeye salmon during each annual run follows a normal distribution. However the mean weight of fish may fluctuate from year to year depending on many ecological and genetic factors. A researcher would like to test whether or not this year’s run has a mean population weight of 5 lb. A random sample of nine fish yielded a mean of 4.7 lb and a standard deviation of 0.5 lb. Test the hypothesis of the researcher at the 5% significance level....
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