The situation is as follows Smart phones have changed the world and how we spend our time A group of researchers at USU want to estimate the mean daily number of minutes that USU students spend on their phones In fall 2019, they took a random sample of 430 USU students and found that on average, students spend 312 minutes on their phones with a standard deviation of 54 minutes per day The plot of the sample data showed no extreme skewness or outliers Calculate a 96 confidence interval estimate for the mean daily number of minutes that USU students spend on their phones in fall 2019 Do not round off in the intermediate steps, only the final answer should be rounded off to two decimal places SHOW YOUR WORK IN ALL THE STEPS ANSWERS WITHOUT SOLUTIONS WILL ONLY GET PARTIAL CREDIT STATE Calculate a 96 confidence interval estimate for the mean daily number of minutes that BYU students spend on their phones in fall 2019 Hide Instructions 1 PLAN State the name of the appropriate estimation procedure (2pts) 2 Describe the parameter of interest in the context of the problem (2pts) 3 SOLVE State the conditions for the procedure and explain how these conditions are met (4pts) 4 Write down the confidence level and the t critical value (2pts) 5 Calculate the margin of error for the interval to two decimal places Show your work Do not round off in the intermediate steps, only the final answer should be rounded off to two decimal places (2pts) 6 Calculate the confidence interval to two decimal places and state it in interval form (2pts) 7 CONCLUDE Interpret your confidence interval in context Do this by including these three parts in your conclusion (3 pts) Level of confidence (1pt) Parameter of interest in context (1 pt) The calculated interval (1 pt) 8 FURTHER ANALYSIS How would selecting a 90 level of confidence change the width of the calculated confidence interval (1pt) Explain or justify your answer by recalculating, rounded to two decimal places (1pt) Do not round off in the intermediate steps, only the final answer should be rounded off to two decimal places 9 At a 90 level of confidence, what sample size would be needed to estimate the parameter of interest to within a margin of error of 10 minutes Use 56 minutes (2pts) 10 Suppose that a second random sample of USU students was conducted in fall 2019 Using this data, the 96 confidence interval was calculated to be (310 92, 317 58) Rounded to two decimal places , what is the margin of error for this confidence interval Show your work (1pt)

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The situation is as follows: Smart phones have changed the world and how we spend our time. A group of researchers at USU want to

The situation is as follows:

Smart phones have changed the world and how we spend our time. A group of researchers at USU want to estimate the mean daily number of minutes that USU students spend on their phones. In fall 2019, they took a random sample of 430 USU students and found that on average, students spend 312 minutes on their phones with a standard deviation of 54 minutes per day. The plot of the sample data showed no extreme skewness or outliers. Calculate a 96% confidence interval estimate for the mean daily number of minutes that USU students spend on their phones in fall 2019. Do not round off in the intermediate steps, only the final answer should be rounded off to two decimal places.

SHOW YOUR WORK IN ALL THE STEPS. ANSWERS WITHOUT SOLUTIONS WILL ONLY GET PARTIAL CREDIT.

STATE

Calculate a 96% confidence interval estimate for the mean daily number of minutes that BYU students spend on their phones in fall 2019.

Hide Instructions

PLAN:

State the name of the appropriate estimation procedure. (2pts)

Describe the parameter of interest in the context of the problem. (2pts)

SOLVE:

State the conditions for the procedure and explain how these conditions are met. (4pts)

Write down the confidence level and the t* critical value. (2pts)

Calculate the margin of error for the interval to two decimal places. Show your work. Do not round off in the intermediate steps, only the final answer should be rounded off to two decimal places. (2pts)

Calculate the confidence interval to two decimal places and state it in interval form. (2pts)

CONCLUDE

Interpret your confidence interval in context. Do this by including these three parts in your conclusion (3 pts):

Level of confidence (1pt)
Parameter of interest in context (1 pt)
The calculated interval (1 pt)

FURTHER ANALYSIS

How would selecting a 90% level of confidence change the width of the calculated confidence interval? (1pt). Explain or justify your answer by recalculating, rounded to two decimal places (1pt). Do not round off in the intermediate steps, only the final answer should be rounded off to two decimal places.

At a 90% level of confidence, what sample size would be needed to estimate the parameter of interest to within a margin of error of 10 minutes? Use = 56 minutes. (2pts)

10.

Suppose that a second random sample of USU students was conducted in fall 2019. Using this data, the 96% confidence interval was calculated to be (310.92, 317.58). Rounded to two decimal places, what is the margin of error for this confidence interval? Show your work. (1pt)