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A company offers the service of doing the paperwork associated with claiming tax back for workers....

A company offers the service of doing the paperwork associated with claiming tax back for workers. They claim in an advertising campaign that the average amount their clients receive is £450. A survey of 150 randomly selected clients of the company recorded the amount that each received and the average was £383 with a standard deviation of £93.

i. Construct a 99% confidence interval.

ii. Interpret the interval and discuss the validity of the claim made by the company.

iii. A graph of the raw data indicated that the data came from a population with a distribution that was skewed to the right. What effect does this have on the validity of the confidence interval and its interpretation?

math   Statistics-And-Probability   
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Answer Date: 23/01/2019 A 99% confidence interval for the mean amount received is, First, compute t-critical value then find confidence interval The t critical value for the 99% confidence interval is. The sample size is small and two-tailed test. Look in the column headed α-001 and the row headed in the t distribution table byusing degree of freedom is d,f.= n-1 = 150-1 -149 The t critical value for the 99% confidence interval is 2.609.-383 2.609 x 93//150 383 +19.81 -363.19 to 402.81 A 99% confidence interval for the mean amount received is l 363.19 to 402.81 Interpretation of confidence interval There are 99% confident that the mean amount received is between £3 63 . 1 9 and £402.81 . The claim of the average amount their clients receive is different from £450 is valid due to a 99% confidence interval for the mean amount received is between £363.19 and £402.81 does not include £450.graph of the raw came from a population with a distribution that was skewed to the right. The confidence interval is invalid effect does this have on the validity of the confidence interval and its interpretation

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