Answer:
A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F
Test statistic(Z) = 2.31
P-value = 0.0104
Step-by-step explanation:
Step 1
Null hypothesis: The average damaging temperature of nine iPods is 5°F
Alternate hypothesis: The average damaging temperature of nine iPods differs from 5°F
Step 2
Mean=5°F, Sd=3, df=n-1=9-1=8
The t-value corresponding to 8 degrees of freedom and 95% confidence level (5% significance level) is 2.306
Confidence Interval(CI) = (mean + or - t×sd/√n)
CI = (5 + 2.306×3/√8) = 5 + 6.918/2.828= 5+2.45=7.45°F
CI = (5 - 2.306×3/√8) = 5-2.45 = 2.55°F
Z = (sample mean - population mean)/(sd÷√n) = (5-2.55)/(3÷√8) = 2.45/1.061 = 2.31
Step 3
Using the standard distribution table, the cumulative area to the left of Z = 2.31 is 0.9896
P-value = 1 - 0.9896 = 0.0104
Step 4
Conclusion: A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F
