Question

In a faculty of dentistry, the average durabilitiy of dental fillings made using a particular medication by the assistant as a dissertation. The ?=?? dental fillings made using the medication are selected randomly and the sample mean and the sample stanadart deviation are calculated as; ?̅ =8 year, S= 2.86 year. For the population mean μ, obtain the two sided confidence interval.
Note:
Take the sample mean value from the interval [5,10]
( no digit)
Take the standard deviation value from the interval [1,4] with two digit after the point.
Take the (?−?) value from the 0.90, 0.95, 0.99 most used values. Explain which case you use.

The assistant claim that, the average durability of the dental fillings is different from the ?0 year. ( ???? ?ℎ? ?0 ????? ????????) To test the hypothesis.
a.Write the ?? ve ?? hypothesis
b.Obtain the calculated value.
c.Show the critical region.
d.What is your conclusion

Answer 1

Here the sample size is n = 25

Sample mean = 8 year

Sample standard deviation = S = 2.86 years

Sine the sample size is less than 30, we have to use t distribution

The Confidence interval of population mean at 95% confidence is given by

2nd part of the question

The assistant claim that the average durability of the dental claim is different from year

For the problem we are taking

So we want to test the following Hypothesis

against the alternative

To test this Hypothesis we are first going to calculate the test statistic T which follows t distribtuion with n-1 df i.e. 24 df

The T calculated > T critical at 24 df

So we reject the Null Hypothesis and conclude the claim made by assistant is not statistically correct.