STK143 - Tutorial 5 Worksheet - 2019 PDF

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Summary

This tutorial worksheet tests your knowledge of point estimation....

Description

STK143

Tutorial 5 Worksheet

19 – 21 August 2019

Exercise 1 A simple random sample of 8 months of sales data provided the following information: Month 1 2 3 4 5 6 7 8 Units Sold

94

100

85

94

92

95

88

91

a) Develop a point estimate for the population mean

b) Develop a point estimate for 𝝈

c) Develop a point estimate for 𝒑, the proportion of months in which more than 94 units were sold. Exercise 2 A sample of 50 students showed that 25 students use Samsung, 18 students use iPhone, and the remaining students use phones from other brands. Complete the following table to develop a point estimate for students using phones of different brand Brand

Proportion

Samsung Apple (iPhone) Other Exercise 3 Histograms of the sampling distribution of 𝑋 for samples of size 20 and 200 were prepared. With your knowledge of the sampling distribution of 𝑋, which one was for 𝑛 = 20 and which one was for 𝑛 = 200? Add the sample size to the graphs.

25

20

20

Bin

Bin

1

23

22.5

22

21.5

21

20.5

18

23

22.5

22

21.5

21

0 20.5

0 20

5

19.5

5

19

10

18.5

10

20

15

19

15

18.5

Frequency

25

18

Frequency

n = ………

30

19.5

n = ………

30

Exercise 4 The amount of time that students study outside of lectures (weekly) is normally distributed with a mean of 15 hours and standard deviation of 3 hours. a. What is the probability that a student studies more than 20 hours? b. Find the probability that the average amount of time spent on studying per week for 9 randomly selected students is more than 20 hours per week.

Let 𝑋 =

Let 𝑋 =

Then 𝑋~

Then 𝑋~

Exercise 5 Let 𝑌~𝑡(16). Find the following probabilities/percentiles: a)

𝑃(𝑌 = 1.746) =

b)

𝑃(𝑌 < 2.583) =

c)

𝑃(𝑌 > 0.865) =

d)

𝑃(𝑌 < −2.921) =

e)

𝑃(𝑌 ≥ −1.337) =

f)

𝑃(1.337 < 𝑌 ≤ 2.921) =

g)

Find an approximate interval in which 𝑃(𝑌 > 2.385) lies.

h)

Find an approximate interval in which 𝑃(𝑌 > 0.623) lies.

i)

Find 𝑦 if 𝑃(𝑌 < 𝑦) = 0.95 2...