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?

We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.

See response to your later post.

To test the hypotheses for questions 1-5 using confidence intervals, we will follow these steps:

Step 1: State the hypotheses.
Step 2: Calculate the sample mean and standard error.
Step 3: Determine the critical value.
Step 4: Calculate the confidence interval.
Step 5: Analyze the confidence interval and draw conclusions.

Let's apply these steps to each question.

1) Hypotheses:
Null hypothesis (H0): The mean life of the light bulbs is 1200 hours.
Alternative hypothesis (Ha): The mean life of the light bulbs is not 1200 hours.

Step 2: Calculate the sample mean and standard error:
Sample mean (x̄) = 1050 hours
Standard deviation (s) = 200 hours
Sample size (n) = 100

Standard error (SE) = s / √n
SE = 200 / √100 = 20

Step 3: Determine the critical value:
Since we have a 95% confidence level, the critical value is obtained from a standard normal distribution (Z-distribution) with a two-tailed test. The critical value at 95% confidence level (α = 0.05) is ±1.96.

Step 4: Calculate the confidence interval:
Confidence interval = x̄ ± (Z * SE)
Confidence interval = 1050 ± (1.96 * 20)
Confidence interval = 1050 ± 39.2
Confidence interval = (1010.8, 1089.2)

Step 5: Analyze the confidence interval and draw conclusions:
Since the claim of the light bulb producing company falls within the confidence interval (1200 hours), we fail to reject the null hypothesis. Therefore, the light bulbs are in compliance with the company's claim.

Now let's proceed with the other questions using the same steps.

2) Null hypothesis (H0): The mean employee presence is 4 days per week.
Alternative hypothesis (Ha): The mean employee presence is not 4 days per week.
Calculate the confidence interval, analyze it, and draw conclusions.

3) Null hypothesis (H0): The mean student score is 90.
Alternative hypothesis (Ha): The mean student score is not 90.
Calculate the confidence interval, analyze it, and draw conclusions.

4) Null hypothesis (H0): The mean response time is 10 seconds.
Alternative hypothesis (Ha): The mean response time is not 10 seconds.
Calculate the confidence interval, analyze it, and draw conclusions.

5) Null hypothesis (H0): The mean iodine content is 20 mg.
Alternative hypothesis (Ha): The mean iodine content is not 20 mg.
Calculate the confidence interval, analyze it, and draw conclusions.

To solve each of these questions using confidence intervals, we follow a few steps:

Step 1: State the Hypotheses
In hypothesis testing using confidence intervals, we typically have two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis typically assumes no change or no difference, while the alternative hypothesis challenges the null hypothesis.

Step 2: Determine the Sample Size, Confidence Level, and Standard Deviation
We need to know the sample size, the desired confidence level, and the standard deviation to conduct the hypothesis test using confidence intervals.

Step 3: Calculate the Confidence Interval
Using the sample mean, sample size, and standard deviation, we calculate the confidence interval. The confidence interval represents the range in which the population parameter (mean) is estimated to be based on our sample.

Step 4: Interpret the Confidence Interval
Based on the confidence interval calculated, we can determine whether the sample data supports or rejects the null hypothesis.

Now, let's solve each question using the steps mentioned above:

1) For the first question:
H0: The average life of the light bulbs is equal to 1200 hours.
Ha: The average life of the light bulbs is not equal to 1200 hours.
Sample Size (n) = 100
Confidence Level = 95%
Standard Deviation (σ) = 200
Sample Mean (x̄) = 1050

Calculating the confidence interval:
Confidence Interval = x̄ ± Z * (σ / sqrt(n))

Z represents the critical value based on the confidence level. For a 95% confidence level, Z is approximately 1.96.

Confidence Interval = 1050 ± 1.96 * (200 / sqrt(100))

Now, calculate the lower and upper bounds of the confidence interval.

Interpreting the result:
If the claimed value (1200 hours) falls within the confidence interval, we accept the null hypothesis (H0). If the claimed value lies outside the confidence interval, we reject the null hypothesis.

Repeat steps 2-4 for the remaining questions using the same approach.

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.