· For each question submit an image or pdf of your solution. Each question is to be uploaded separately and each will accept multiple files.
· When the assignment is completed, press Submit at the end of the page
· Do not round any number during calculating, always use the exact number till you get the final answe
Excel Hint for finding critical values:
· Two tailed t test
· Left tailed t test or right tailed t test
1. A group of 8 students are asked to estimate the length of one minute without reference to any timers. The times they provided (in seconds) are given below:
53
67
63
55
75
58
56
62
Assuming the population is approximately normal and using a 0.05 significance level, test the claim that these provided times are indeed from a population with mean 60 seconds.
a) State the null and alternative hypotheses.
) Calculate the test statistic (round it to 3 decimal places).
c) Find the critical value (round it to 3 decimal places).
d) Make a statistical conclusion. Do the results indicate that students are reasonably good at estimating the length of one minute?
2. A professor claims that the mean final mark for is greater than 65. A sample of 35 students shows the sample mean is 67 with standard deviation 15. Test the professor’s claim using a 0.05 significance level.
a) State the null and alternative hypotheses.
) Calculate the test statistic (round it to 3 decimal places).
c) Find the P -value (round it to 3 decimal places).
d) Make a conclusion based on your answers in parts b) and c).
e) Explain what would constitute a Type I e
or in this context.
f) Explain what would constitute a Type II e
or in this context.
3. The data in the table below were obtained through a survey of randomly selected individuals in London
Speeding Tickets Received Within the Last Year?
Yes
No
Male
30
224
Female
27
473
a) Find the probability of getting someone ticketed for speeding, given that the selected person is a man (round to 3 decimal places).
) Find the probability of getting someone ticketed for speeding, given that the selected person is a woman (round to 3 decimal places).
c) Use a 0.01 level of significance to test the claim that men are more likely to receive a speeding ticket than women.
· To use normal approximation, check the sample size requirements
· Calculate the test statistics (round to 3 decimal places).
d) Find the critical value (round it to 3 decimal places).
e) Make a conclusion based on your answer from part c) and d).
4. 10 Healthy adults’ initial temperature (Temp 1) have been measured while sitting still, then their temperatures are measured again after laying down (Temp 2).
Subject
1
2
3
4
5
6
7
8
9
10
11
Temp 1
37.51
37.07
37.20
37.23
37.38
37.59
37.28
37.12
37.55
37.04
37.78
Temp 2
37.17
36.91
36.70
36.80
36.96
37.25
37.11
36.82
37.36
36.92
37.22
a) To test the claim that the mean temperature difference is 0 while sitting still vs. laying down, state the null and alternative hypotheses.
) At significance level, find the critical value (round to 3 decimal places).
c) Calculate the test statistics (round to 3 decimal places).
d) Use Excel Data Analysis function, at 0.05 significance level, compare the two paired sample mean, submit a screenshot of the result output. (t Stat from the output should match your answer in part c).
e) Based on your answer from c) or d), at level, what is your conclusion?
5. Download the excel file “Births” for the data set. It uses the birth weights of boys and girls. Using Excel Data Analysis Tool, test the claim that girls have a lower mean weight than boys at 0.05 level of significance. Do not assume population variances are equal. Hint: Open Excel, Data – Data Analysis. See two pictures below.
a) State the null and alternative hypotheses.
) Find the test statistic (round it to 3 decimal places) from Excel output
c) Find the P -value (round it to 3 decimal places) from Excel output
d) Find critical value from Excel output
e) Make a statistical conclusion based on your answers in parts b) to d).
6. An agent for a real estate company wanted to predict the monthly rent for apartments based on the size of the apartment. The data ”Rent” for a sample of 25 apartments is available for download from Brightspace. Perform a t test for the slope to determine if a significant linear relationship between the size and the rent exists at the 0.05 level of significance.
a) Create a scatter plot using Excel. Using your official name as the chart title.
) Use Excel CORREL to find the linear co
elation coefficient r.
c) Find test statistic from Excel Summary Output.
d) Find p-value from Excel Summary Output
e) Make a statistical conclusion based on your answers in parts c) and d).
Note 1, for c) and d), please submit your Excel Summary Output.
Note 2, hint for using Regression using Excel:
Girls
Girl BIRTH WEIGHT Boy BIRTH WEIGHT
3500 3900
800 2800
2400 3700
4200 4000
3100 3400
2000 1600
2900 3500
3300 3900
2800 3000
2500 3200
4000 3300
3100 300
3000 4000
3400 4500
3500 3600
1500 1700
1600 3900
900 3800
3800 2200
2100 1800
2600 3500
4300 3400
3400 3000
3300 4100
3500 4100
3000 2700
3500 2900
2900 3300
3300 2800
2500 3500
2800 3700
2800 3600
3500 3300
900 3700
2700 4300
3700 2600
3500 3300
3000 3200
3400 3900
4700 3600
3300 3400
2800 4100
3300 3300
3100 1500
2400 2600
4200 3300
3200 3600
2300 3800
2900 2000
3100 3000
2700 3800
4200 3600
3500 3100
3000 1500
4000 600
3600 1000
3200 3200
3500 3800
2400 3900
3100 3600
2800 3400
3800 3200
2500 3600
3100 3400
3500 3600
3700 2700
3500 3500
4300 3600
2500 3400
3100 3800
3800 3400
2800 3400
3000 2700
3600 2900
2700 4100
3300 4300
2700 3500
3700 3100
3200 3400
3800 3600
2800 3800
3600 2800
2500 4900
2600 3800
3200 3600
2600 3000
3300 3200
3300 3700
2900 3400
2900 4000
3100 3900
3000 2500
1900 2800
3100 3300
3100 2900
4300 3700
3200 3300
1800 3600
3200 3100
3000 3300
3000 3500
3200 2700
3300 3700
3100 4000
3200 3700
2600 2300
3800 2900
3200 3300
3400 2600
2300 2400
3500 3300
2600 3200
3100 3800
2800 2900
3300 3400
3000 3300
3200 2700
3400 3300
2300 3000
2900 2900
2800 3900
1900 4000
3600 2900
3600 3500
4100 3700
2200 3500
3800 3800
3000 3600
3100 4000
2600 3200
3400 3600
2000 4100
3100 3500
3600 3400
1700 3300
3300 3100
3300 4000
3700 3200
3400 2700
3100 3200
3800 3100
2600 3500
3600 3700
3600 3400
3000 3600
2800 3600
2900 3000
3600 3100
2300 3500
300 2900
3300 3600
3300 3300
3400 3000
2800 3300
3400 4000
1800 2700
2400 3400
2800 2900
2900 2800
2700 3400
3300 2300
2900 2900
3600 2400
3600 3600
4600 3500
3100 3500
700 3800
2600 2700
2000 4000
3300 2300
2000 3600
3700 4500
3100 3300
3600 2700
1600 2600
3000 3700
2700 1600
3200 3900
4000 3100
3400 4600
3800 2500
3700 3600
3400 3400
3300 3200
2400 2800
3600 2800
2200 4300
3100 3300
2800 2800
3700 2900
3400 3300
3100 3500
3200 3200
2400 3400
800 3200
2400
3500
1700
3000
3500
2900
3400
4000
3200
4000
Sheet1
Size_(sq._ft) Rent_($)
840 1975
1440 2650
1085 2175
1242 2500
728 1975
1495 2700
1126 2675
736 1935
690 1900
966 2125
1110 2400
1285 2625
1975 3275
1369 2800
1165 2400
1235 2475
1235 2075
1249 2700
1150 2200
906 2175
1361 2600
1030 2675
765 2175
990 1800
1200 2750