459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.

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459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.

Statistic Assignment.

Title: Confidence Intervals

1.459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.

Find the critical value for zα/2 that corresponds to a degree of confidence of 98%.
Find the margin of error for the 95% confidence interval used to estimate the population proportion with n = 163 and x = 96.
Construct the confidence interval for question 3.
Interpret the confidence interval found in question 4.
What are the requirements for a Student’s t-distribution?
Find the critical value for tα/2 corresponding to n = 12 and 95% confidence level.
Use the confidence level and sample data to find the margin of error E.
College students’ annual earnings:

99% confidence, n = 81, = $3967, s = $874

Construct the confidence interval for question 8 above.

Interpret and describe the confidence obtained in question 9 in non-technical terms.
Attachments:

statistics_math_assgn._one.docx