Texts: A New York Times article noted that the mean lifespan for 25 male symphony conductors was 73.4 years, in contrast to the mean of 69.5 years for males in the general population. Assuming that the 25 males have lifespans with a standard deviation of 8.7 years, use a 0.05 significance level to test the claim that male symphony conductors have a mean lifespan that is different from 69.5 years. Include all steps for all points.
1. Label and describe the parameter of interest.
The parameter of interest is the mean lifespan of male symphony conductors.
2. State the null hypothesis.
The null hypothesis is that the mean lifespan of male symphony conductors is equal to 69.5 years.
3. State the alternative hypothesis.
The alternative hypothesis is that the mean lifespan of male symphony conductors is different from 69.5 years.
4. What test statistic should be used?
Since we are comparing the mean lifespan of male symphony conductors to a known value (69.5 years) and have a sample size of 25, we should use a t-test.
5. Calculate the numerical value of the test statistic.
To calculate the test statistic, we need the sample mean, the population mean, the sample standard deviation, and the sample size. The sample mean is 73.4 years, the population mean is 69.5 years, the sample standard deviation is 8.7 years, and the sample size is 25. Using these values, we can calculate the test statistic.
6. Calculate the p-value for the test based on the numerical value of the test statistic.
To calculate the p-value, we need to compare the test statistic to the t-distribution with degrees of freedom equal to the sample size minus 1. Using the test statistic and the degrees of freedom, we can find the p-value associated with the test.
Note: The specific calculations for the test statistic and p-value are not provided in the given text.