The mean interest rate for credit cards was reported to be 18.8. A financial officer wishes to study whether the increased competition in the credit card business has reduced interest rates. A sample of 15 credit card is randomly selected and the interest rates are found to be: 18, 13, 14, 13.5, 12.2, 15, 15.4, 12.8, 14.6, 16, 15.8, 16.5, 13.8, 17, 14.8 a) State the appropriate hypotheses to test whether the increased competition in the credit card business has reduced interest rates. [2 marks] b) Determine the mean and standard deviation of the sample of credit card interest rates. [3 marks] c) Test the hypotheses stated in part (a) at a 5% level of significance, and comment on your findings. [5 marks]
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Problem 4
The
18, 13, 14, 13.5, 12.2, 15, 15.4, 12.8, 14.6, 16, 15.8, 16.5, 13.8, 17, 14.8
a) State the appropriate hypotheses to test whether the increased competition in the credit card business has reduced interest rates. [2 marks]
b) Determine the mean and standard deviation of the sample of credit card interest rates. [3 marks]
c) Test the hypotheses stated in part (a) at a 5% level of significance, and comment on your findings. [5 marks]
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