Credit Card Limits

Credit card companies use a regression model (includes such factors as income, employment, credit history) to determine the credit worthiness of a prospective card holder. In the past, the companies used a threshold (cutoff) limit of 630 to receive a card. It is also assumed that the standard deviation of all potential credit card holders is 5. Recent information suggests that delinquencies have been increasing and it is hypothesized that credit card companies will raise the “cutoff score” in response. Examine the results concerning “cutoff scores” from 44 credit card issuers (Table 1) to determine, at the 10% level, if there is evidence that the “cutoff score” has been increased significantly from 630.

Table 1: Summary statistics for the ‘cutoff’ scores for credit card issuers.

Variable   Mean  Median StDev  Min  Max    Q1     Q3
CCards   636.86  636.50  4.42  629  647  633.25 640.00

Length of Northern Pike

Owens and Pronin (2000) studied the age and growth of pike (Esox lucius) in Chivyrkui Bay on Lake Baikal. They found that the length of the sample of 30 pike in Lake Baikal was slightly right-skewed with a mean of 656.1 mm. Suppose that a recent article in an outdoor magazine reported the average length of all pike in this lake to be 600 mm long. It is known from previous studies that the standard deviation of pike length is about 130 mm. Perform a test, using a 95% confidence level, to determine if the mean length of pike reported by the researchers significantly differs from that reported in the outdoor magazine.

Chronic Myofascial Pain Syndrome

A study by Cheshire et al. (1994) reported on six patients with chronic myofascial pain syndrome. Summary statistics from the six individuals is in Table 2. Test the hypothesis that the mean pain length was greater than 2.5 years at the 10% significance level. Assume that it is known that the distribution of duration of pain is normal with a standard deviation of 0.5 years.

Table 2: Summary statistics for pain length for patients with chronic myofascial pain syndrome.

     n   mean     sd    min     Q1 median     Q3    max 
  6.00   2.77   0.16   2.50   2.73   2.80   2.80   3.00 

Cholesterol Levels

Suppose that it is known that cholesterol levels in women aged 21-40 in the U.S. has a mean of 190 mg/dl and standard deviation of 40 mg/dl. Suppose that we want to determine, at the 10% significance level, if the cholesterol level of Asian women is different from U.S. women as determined from 40 randomly selected Asian women aged 21-40 who had recently immigrated to the U.S. Assume that the Asian women have the same standard deviation as the U.S. women population. The summary statistics from this sample are in Table 3.

Table 3: Summary statistics for the cholesterol level of Asian women aged 21-40 that had recently immigrated to the U.S.

     n   mean     sd    min     Q1 median     Q3    max 
 40.00 180.55  40.86 100.30 160.38 180.20 200.45 289.00