Reference no: EM132844991
1. In the Philippine legal system, a defendant is presumed innocent until proven guilty. Consider a null hypothesis, H0, that the defendant is innocent, and an alternative hypothesis, H1, that the defendant is guilty. A jury has two possible decisions: Convict the defendant (i.e., reject the null hypothesis) or do not convict the defendant (i.e., do not reject the null hypothesis).
Explain the meaning of the risks of committing either a Type I or Type II error in this example.
2. The quality-control manager at a light bulb factory needs to determine whether the mean life of
a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?
b. Compute the p-value and interpret its meaning.
c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.
d. Compare the results of (a) and (c). What conclusions do you reach?
3. A fast food file contains the amount that a sample of nine customers spent for lunch ($) at a fast-food restaurant:
4. 20 5.03 5.86 6.45 7.38 7.54 8.46 8.47 9.87
a. At the 0.05 level of significance, is there evidence that the mean amount spent for lunch is different from $6.50?
b. Determine the p-value in (a) and interpret its meaning.
c. What assumption must you make about the population distribution in order to conduct the t test in (a) and (b)?
d. Because the sample size is 9, do you need to be concerned about the shape of the population distribution when conducting the t test in (a)? Explain