1. A golfer claims that his average golf score at the course he plays regularly is less than 6.5. A random sample of 35 rounds of golf was selected from a total 250 rounds that were played at the golf course (Population size N=250). The sample mean obtained was 6.028. Assume that the standard deviation for the population of scores for this golfer is 0.557 and a significance level α = 5%. What is the observed value of the test statistic z for the hypothesis test ?
2. Sony would like to estimate the average age of a PlayStation user and collects a random sample of 20 PlayStation users. The PlayStation users in the sample had an average age of 16.4 years and a standard deviation of 2.1 years. What is the margin of error of the 95% confidence interval for the the average age of PlayStation users ? (Use 3 decimal places for your response)
3. The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 20 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.54 and 0.1 inches, respectively. Using a 10% significance level, the appropriate decision is _______.
a. Reject the null hypothesis and shut down the punch
b. Do NOT reject the null hypothesis and shut down the punch
c. Do NOT reject the null hypothesis and do not shut down the punch
d. Reject the null hypothesis and do not shut down the punch