Extra Exercise: Estimation and Hypothesis Testing
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.
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?
A sample of 8 independent observations provides the following:
Can you conclude at 5% level of significance that the mean is below 5?
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.
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.
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.
Number with 0 cavities
Based on these sample data and using a significance level of 0.05, what...
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