Statistics and Significance Level

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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.

8.028.008.018.017.998.007.998.038.01

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:

3.63.93.84.54.94.24.43.8

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.

AdultsChildren
Sample Size 100 200
Number with 0 cavities 83 165

Based on these sample data and using a significance level of 0.05, what...
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