St Thomas More Catholic Secondary School

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MATH

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MATH-4U1

Question 1

 A study asked 10425 random Canadians if they have a predominant left hand. It found out that 1142 were predominantly left-handed individuals. Find a 98% confidence interval for the population of Canadian who are left-handed. Ensure to check for normality and test whether the sample size is valid. The Canadian population is 40, 528, 396 (taken from Statistics Canada). Write down the formulas used.

Question 2 

A study gathered a simple random sample that included 24 St. Catharines residents and concluded that their mean weight is 61kg with standard deviation of 3.88kg. Construct 90% confidence interval for St. Catharines residents's mean weight. Ensure to check for normality and test whether the sample size is valid. The population of St. Catharines is said to be 136, 803 (taken from www.stcatharines.ca). Write down the formulas used

Question 3

 The mean IQ score of Brock University students is 99. The IQ score of 36 Brock University's STAT 1F92 students have a mean of 96 along with a standard deviation of 7.61. Assuming the STAT 1F92 students is a simple random sample and α = 0.025 as the level of significance, determine if there is evidence to suggest that Brock University's STAT 1F92 students tend to be below Brock University's average IQ. Use the classical approach and the P-value approach. For this question, don't test for normality nor sample size. Write the formulas used and mention whether it is a left-tail, right-tail or two-tailed test.

Question 4

It is true that St. Catharines residents prefer cars over trucks? A survey asked all St. Catharines residents and concluded that 41% of them prefer a car over a truck. In 2024, a new survey randomly selected 106 residents who are bus drivers and realized that 34 of them prefer to drive a truck. With a level of significance of 0.05, does the new survey suggest the proportion of bus drivers choose a vehicle that is different than St. Catharines residents? Use the classical approach and the P-value approach. For this question, don't test for normality nor sample size. Write the formulas used and mention whether it is a left-tail, right-tail or two-tailed test. 

Question 5

An organization that packages bananas disclosed that the weight standard deviation of their banana box packing is 0.52kg. A new proposal was passed by the management to use biodegradable packaging. They are afraid that the new change would result in less consistent packaging. A sample of 15 packages was chosen which had a variance of 0.43kg. Conduct the appropriate test at α = 0.01 level of significance. Use the classical approach and the P-value approach. For this question, don't test for normality nor sample size. Write the formulas used and mention whether it is a left-tail, right-tail or two-tailed test. 

Question 6

 Suppose the average age of a person in this world is 31.70 years. A randomly chosen sample of size 81 from St. Catharines residents has a mean of 32.91 years along with a standard deviation of 4.59 years. With α = 0.05 level of significance, determine if there is sufficient evidence to conclude that St. Catharines residents have different age average than the typical age. Use the classical approach and the P-value approach. For this question, don't test for normality nor sample size. Write the formulas used and mention whether it is a left-tail, right-tail or two-tailed test. 

PLEASE INCLUDE ALL STEPS TO ALL ANSWERS INCLUDING ALL FORMULAS USED.  PLEASE DO NOT TELL ME TO DO IT MYSELF AFTER GIVING ME THE FORMULAS