Probability and Statistics

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For questions 1- 5 use confidence intervals to test the hypothesis.

1) A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours. A sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours. At a 95% confidence level, determine whether these light bulbs are in compliance with the company's claim.

2) A company's human resource department claims that all employees are present on the average 4 days out of the work week with a standard deviation of 1. They hired an outside company to do an audit of their employees' absences. The company took a sample a 10 people and found that on the average the employees were present 3 days per week. With a 95% confidence level, determine whether the company's claim is true based on the data from the sample.

3) A teacher claims that all of her students pass the state mandated test with an average of 90 with a standard deviation of 10. The principal gave the test to 20 of her students to see if the teacher's claim was true. He found that the average score was 75. With a 95% confidence level, determine whether the teacher is making the correct claim about all of her students.

4) The lifeguard's at a local pool have to be able to respond to a distressed swimmer at an average of 10 seconds with a standard deviation of 4 in order to be considered for employment. If a sample of 100 lifeguards showed that their average response time is 15 seconds, with a confidence level of 95% determine whether this group may be considered for employment.

5) It is believed that an average of 20 mg of iodine is in each antibiotic cream produced by a certain company with a standard deviation of 5 mg. The company pulled 150 of its antibiotic creams and found that on the average each cream contained 29 mg of iodine. Determine with a 95% confidence level whether or not these creams are in compliance with the company's belief?

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  • Probability and Statistics -

    1)  A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours.  A sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours.  At a 95% confidence level, determine whether these light bulbs are in compliance with the company's claim.

    1050 is outside of the confidence interval, which means that we must reject the null hypothesis and conclude that the average life of each lightbulb reported by the company is incorrect.
    2)  A company's human resource department claims that all employees are present on the average 4 days out of the work week with a standard deviation of 1.  They hired an outside company to do an audit of their employees' absences.  The company took a sample a 10 people and found that on the average the employees were present 3 days per week.  With a 95% confidence level, determine whether the company's claim is true based on the data from the sample.

    2.285 - 3.715

    The company's claim is true because 3 is within the confidence interval, concluding that employees are present 3 days per week.

    3)  A teacher claims that all of her students pass the state mandated test with an average of 90 with a standard deviation of  10.  The principal gave the test to 20 of her students to see if the teacher's claim was true.  He found that the average score was 75.  With a 95% confidence level, determine whether the teacher is making the correct claim about all of her students.

    70.32-79.68

    75 falls inside the confidence interval.

    The teacher's students are passing the tests with an average of 75% instead of 90%.

    Concluding that the teacher is not making the correct claim about the percentage the students are making, but that her students are passing the mandated tests in general.  

    4)  The lifeguard's at a local pool have to be able to respond to a distressed swimmer at an average of 10 seconds with a standard deviation of 4 in order to be considered for employment.  If a sample of 100 lifeguards showed that their average response time is 15 seconds, with a confidence level of 95% determine whether this group may be considered for employment.

    14.21-15.79

    15 secounds falls within the confidence interval making the group not considerable because the lifeguards have to be able to respond to a distressed swimmer at the average of 10 seconds, not 15. 

    5)  It is believed that an average of  20 mg of iodine is in each antibiotic cream produced by a certain company with a standard deviation of 5 mg.  The company pulled 150 of its antibiotic creams and found that on the average each cream contained 29 mg of iodine.  Determine with a 95% confidence level whether or not these creams are in compliance with the company's belief?

    28.19-29.81

    29 falls within the confidence interval, making the creams not in compliance with the company's belief. 

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