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 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]
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