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STA1010 - Statistical methods for science - S2 2025

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Determine the P-value.

A student runs an experiment to determine the number of joules of energy three different people burn by running a kilometre. Each of the 3 subjects runs the kilometre 4 times. The F-ratio obtained is 4.50. Use MS Excel or a graphics calculator for the appropriate F-distribution.

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In a study involving 4 treatment groups, and numerous trials done in each, the variances gave the totals of : SST=25.8 and SSE=145.7 for dfT=3 and dfE=31.

Consider the mean squares and calculate the F-statistic for this data?

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When a one-way analysis of variance test is done, what probability distribution is used to find the p-value?

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The university wanted to know if there was a difference in the mean daily hours of study for students enrolled in different faculties.  A random sample of 1000 students from each of the four major faculties was taken and the average time in study was determined for each faculty.

What is the null hypothesis for this situation?
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In carrying out a chi-square test of independence for a table of data with 5 rows and 3 columns,  the test statistic  is calculated to be  16.5. The P-value is closest to

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A study examined the survival of patients with heart disease and pet ownership. Each patient with heart disease was classified as having a pet or not and whether they survived for one year.

The data are given below.

PetOwnership
Patient statusNoYes
Alive2450
Dead105

 

Assuming no relationship between pet ownership and survival of patients, calculate  (correct to 1 decimal place) the chi-square statistic.

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Interpret the results of the chi-square test at the 5% significance level.

The Book Industry Study Group, Inc., performs sample surveys to obtain information on characteristics of book readers. A book reader is defined to be one who read one or more books in the six months prior to the survey; a non-book reader is defined to be one who read newspapers or magazines but no books in the six months prior to the survey; a nonreader is defined to be one who did not read a book, newspaper, or magazine in the six months prior to the survey. The following data were obtained from a random sample of 1429 persons 16 years old and over.

χ2 = 114.534; P-value = 2.287 × 10-22

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A study examined the survival of patients with heart disease and pet ownership. Each patient with heart disease was classified as having a pet or not and whether they survived for one year.

The data are given below.

PetOwnership
Patient statusNoYes
Alive2750
Dead115

 

Assuming no relationship between pet ownership and survival of patients, what is the expected number  (correct to 1 decimal place) of patients who  have a pet and survived for one year?

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A study examined the survival of patients with heart disease and pet ownership. Each patient with heart disease was classified as having a pet or not and whether they survived for one year.

The data are given below.

PetOwnership
Patient statusNoYes
Alive[x]50
Dead105

In carrying out a chi-square test assuming no relationship between pet ownership and survival of patients, how many degrees of freedom are there?

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