GlitterGayness

18.06.2020 • 

Mathematics

Suppose you observe a sample data set consisting of =64 inter-arrival times 1,…,64 for the subway, measured in minutes. As before, we assume the statistical model that 1,…,64∼exp() for some unknown parameter >0. In this data set, you observe that the sample mean is 164∑64=1=7.8.Additional Instructions: For best results, please adhere to the following guidelines and reminders:For the upcoming calculations, please truncate /2 at 2 decimal places, instead of a more exact value. For example, if /2=3.84941, use 3.84 instead of 3.85 or 3.849.Input answers truncated at 4 decimal places. For example, if your calculations yield 11.327458, use 11.3274 instead of 11.3275 or 11.32745.You will be computing CIs at asymptotic level 90%.Using the ‘solve method' (refer to the slide ‘Three solutions'), construct a confidence interval I solve with asymptotic level 90% for the unknown parameter .[ , ]Using the ‘plug-in method' I plug-in (refer to the slide ‘Three solutions'), construct a confidence interval with asymptotic level 90% for the unknown parameter .[ , ]Which interval is narrower?I solve orI plug-in?Which of these confidence intervals is centered about the sample estimate, lamba hat sub n?i solveI plug-inBothNeither?

Ответ:

Bettie55

18.06.2020

Mathematics

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a)

And using a calculator, excel or the normal standard table we have that:

b)

And using a calculator, excel or the normal standard table we have that:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the interpupillary distance of a population, and for this case we know the distribution for X is given by:

 

Where  and

Part a

Since the distribution for X is normal then we know that the distribution for the sample mean  is given by:

We want to find this probability:

And using a calculator, excel or the normal standard table we have that:

Part b

And using a calculator, excel or the normal standard table we have that:

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Ответ:

bmharris8262

15.12.2021

Mathematics

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C

Step-by-step explanation:

I hope this helps

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