Statistics and Significance Level
Extra Exercise: Estimation and Hypothesis Testing
1. The length (in millimetres) of a batch of 9 screws was selected at random from a large consignment and found to have the following information.
8.02 8.00 8.01 8.01 7.99 8.00 7.99 8.03 8.01
Construct a 95% confidence interval to estimate the true average length of the screws for the whole consignment.
From a second large consignment, another 16 screws are selected at random and their mean and standard deviation found to be 7.992 mm and 0.01mm. Can you conclude at 5% level of significance that the first batch of screws has greater mean than the second batch?
2. A sample of 8 independent observations provides the following:
3.6 3.9 3.8 4.5 4.9 4.2 4.4 3.8
Can you conclude at 5% level of significance that the mean is below 5?
3. A house cleaning service claims that they can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours.
(i) Construct a 95% confidence interval for the population mean of cleaning times.
(ii) Conduct a hypothesis testing by using 0.05 level of significant to verify the claim.
4. A maker of toothpaste is interested in testing whether the proportion of adults (over age 18) who use their toothpaste and have no cavities within a six-month period is any different than the proportion of children (18 and under) who use the toothpaste and have no cavities within a six-month period. To test this, they have selected a sample of adults and a sample of children randomly from the population of those customers who use their tooth paste. The following results were observed. Adults Children Sample Size 100 200 Number with 0 cavities 83 165
Based on these sample data and using a significance level of 0.05, what
1. The length (in millimetres) of a batch of 9 screws was selected at random from a large consignment and found to have the following information.
8.02 8.00 8.01 8.01 7.99 8.00 7.99 8.03 8.01
Construct a 95% confidence interval to estimate the true average length of the screws for the whole consignment.
From a second large consignment, another 16 screws are selected at random and their mean and standard deviation found to be 7.992 mm and 0.01mm. Can you conclude at 5% level of significance that the first batch of screws has greater mean than the second batch?
2. A sample of 8 independent observations provides the following:
3.6 3.9 3.8 4.5 4.9 4.2 4.4 3.8
Can you conclude at 5% level of significance that the mean is below 5?
3. A house cleaning service claims that they can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours.
(i) Construct a 95% confidence interval for the population mean of cleaning times.
(ii) Conduct a hypothesis testing by using 0.05 level of significant to verify the claim.
4. A maker of toothpaste is interested in testing whether the proportion of adults (over age 18) who use their toothpaste and have no cavities within a six-month period is any different than the proportion of children (18 and under) who use the toothpaste and have no cavities within a six-month period. To test this, they have selected a sample of adults and a sample of children randomly from the population of those customers who use their tooth paste. The following results were observed. Adults Children Sample Size 100 200 Number with 0 cavities 83 165
Based on these sample data and using a significance level of 0.05, what