Question Type 6: Performing the chi-squared test for data categorization such that the expected frequency is at least 5 Exercises

A manufacturer claims that 40% of its light bulbs last at least 800 hours, 35% last between 500 and 799 hours, and 25% last less than 500 hours. In a test of 200 bulbs, 68 lasted ≥800 h, 70 lasted 500–799 h, and 62 lasted <500 h. Test the claim at the 5% level.

A retailer claims that 20% of customers choose brand A, 30% brand B, 25% brand C, and 25% brand D. In a random sample of 200 purchases, counts are 38, 64, 50, and 48 respectively. Test the claim at 5%.

In a marketing survey of 180 respondents, three age groups (18–29, 30–49, 50+) and preference for online shopping (Yes, No) are recorded:

A survey of 120 high school students recorded their favorite subject (Math, Science, English, History) and gender:

A random sample of 160 drivers is classified by vehicle type (Car, SUV, Truck) and cellphone use (Yes, No):

A psychologist classifies 140 subjects by coping style (Problem-focused, Emotion-focused, Avoidant) into low, medium, or high stress levels:

In a study of 200 patients, blood type (A, B, AB, O) and presence of a certain antibody (positive or negative) were recorded:

In a genetics experiment, 120 plants are classified by flower color: purple, pink, or white. The expected Mendelian ratio is 9 : 3 : 4. Observed counts are 54 purple, 20 pink, 46 white. Test at 5% whether the data fit this ratio.