# Statistical Analysis of Various Research Studies

## One-Sample t-test

### – A study was conducted to investigate whether the age of tourists in Katatonia has increased since 1995.

In a random sample of 250 tourists in Katatonia, the average age was 47.77 years (s = 15.41 years). This is higher than the average age of 45 years recorded in 1995, and a one-sample t-test shows that this difference in mean age is significant, *t*(249) = 2.84, *p* = .005. The 95% confidence interval indicates that since 1995 the average age of tourists has increased between 0.85 and 4.69 years.

As expected, the age of tourists in Katatonia has increased since 1995.

### – A study was conducted to investigate whether the age of tourists in Katatonia has increased since 1995.

In a random sample of 250 tourists in Katatonia, the average age was 41.43 years (s = 15.93 years). This is lower than the average age of 45 years recorded in 1995, and a one-sample t-test shows that this difference in mean age is significant, *t*(249) = 3.55, *p*

Contrary to expectations, the age of tourists in Katatonia has decreased since 1995.

### – A study was conducted to investigate whether the age of tourists in Katatonia has increased since 1995.

In a random sample of 250 tourists in Katatonia, the average age was 44.84 years (s = 9.96 years). While this is lower than the average age of 45 years recorded in 1995, a one-sample t-test shows that this difference in mean age is not significant, *t*(249) = 0.25, *p* = .805. The 95% confidence interval indicates that since 1995 the average age of tourists is between 6.41 years younger and 6.09 years older than it was in 1995.

There is insufficient evidence to conclude that the age of tourists in Katatonia has increased since 1995.

## Binomial test

### – A study was conducted to explore whether the percentage of Australians using a computer at home has increased since the census in 2001.

In a random sample of 100 adult Australians, 54% had used a computer at home in the previous week. This is higher than the percentage of Australians who reported using a computer at home in the 2001 census (42%), and a Binomial test shows that the difference is significant, *n = *100*, p* = .010. The 95% confidence interval indicates that between 44% and 64% of adult Australians use a computer at home.

As expected, the percentage of Australians using a computer at home has increased since 2001.

### – A study was conducted to explore whether Kayden Real Estate rent more than 35% of their rental properties to families.

In a random sample of 70 rental properties, only 24% were rented to families. This is less than that claimed by Kayden (35%), and a Binomial test shows that the difference is significant, *n = *70*, p* = .037. The 95% confidence interval indicates that between 14% and 34% of Kayden rental properties are rented to families

Contrary to the claims made by Kayden, less than 35% of their properties are rented to families.

### – Researchers suggested that the proportion of Australians who are married has decreased since the 1980s.

In a sample of 416 adult Australians, 67.5% were married. While this is lower than the percentage of Australians who were married in the 1980s (71%), a Binomial test shows that the difference is not significant, *n = *416*, p* = .068. The 95% confidence interval indicates that between 63% and 72% of adult Australians use a computer at home.

There is insufficient evidence to conclude that the proportion of Australians who are married has decreased since the 1980s.

## Independent samples t-test

### – A researcher hypothesised that the blood cholesterol levels of people who do not exercise regularly would be higher than those of regular exercisers.

In a random sample of 78 adults, the average blood cholesterol level of the non-exercisers

(247.65mg/dL, *s = *33.44mg/dL, *n* = 43) was higher than the average blood cholesterol level of the people who exercise regularly ( 189.06mg/dL, *s* = 35.96mg/dL, *n* = 35), and an independent samples t-test shows that this difference in mean blood cholesterol level is significant, *t*(76) = 7.44, *p*

As expected, the blood cholesterol levels of non-exercisers are higher than for those people who exercise regularly.

### – A junior athletics coach hypothesised that the time taken to run 25 metres (in seconds) by children from Easterly Primary School would be shorter than for children from Northhaven Primary School.

In a random sample of 50 Year 8 students, the mean time taken to run 25 metres by the Easterly children ( 12.32 sec, *s =* 4.25 sec, *n =* 25) was more than the mean time taken to run 25 metres by the Northhaven children ( 8.20 sec, *s =* 3.97 sec, *n =* 25), and an independent samples t-test shows that this difference in mean time taken to run 25 metres is significant, *t*(48) = 3.54, *p *= .001. The 95% confidence interval indicates that, on average, Easterly children run this distance between 2 and 6 less seconds slower than Northhaven children.

Contrary to expectations, the time taken to run 25 metres by children from Easterly Primary School was longer than for children from Northhaven Primary School.

### – It was suggested that drivers in the Northern suburbs use more fuel than those in the Western suburbs.

In a sample of 100 drivers, the average fuel consumption for those from the Northern suburbs

( litres, litres, ) was greater than the average fuel consumption for drivers from the Western suburbs ( litres, litres, ). However, an independent samples t-test shows that this difference in mean fuel consumption is not significant, , *p* = .105. The 95% confidence interval indicates that on average fuel consumption is between .59 litres less and 6.14 litres more in the Northern suburbs than in the Western suburbs.

There is insufficient evidence to suggest that fuel consumption is higher for drivers in the Northern suburbs than in the Western suburbs.

## Paired samples t-test

### – It was hypothesised that hypnosis would help reduce the number of cigarettes smoked.

In a sample of 20 smokers, on average the number of cigarettes smoked in the week after

hypnosis was lower ( = 143.70, *s* = 46.75) than the number of cigarettes smoked in the week before hypnosis ( = 180.70, *s* = 64.36). A paired samples t-test shows that this difference in mean number of cigarettes smoked (, *s _{d }* = 27.83) is significant,

*t*(19) = 5.95,

*p*

As expected, hypnosis reduces the number of cigarettes smoked.

-It was hypothesised that tourists visiting the zoo would spend longer viewing the primates than they would viewing the reptiles.

In a sample of 20 tourists, on average, the time spent viewing the primates ( = 62.56 min,

*s *= 12.63 min) was less than the time they spent viewing the reptiles ( = 72.49 min, *s *= 17.48 min), and a paired samples t-test shows that this difference in mean viewing time (*d *= 9.93 min, *sd *= 15.07 min) is significant, *t*(19) = 2.95, *p *= .008. The 95% confidence interval indicates that, on average, tourists visiting the zoo spend between 3 and 17 minutes less viewing the primates than viewing the reptiles.

Contrary to expectations, tourists visiting the zoo spend less time viewing the primates than they spend viewing the reptiles.

-It was hypothesised that the blood cholesterol levels in people with heart disease could be lowered by introducing plant sterols into the diet.

In a random sample of 26 people with heart disease, on average, blood cholesterol levels were lower after sterols were added to the diet ( = 255.45, *s* = 40.30) than before ( = 260.60, *s* = 34.13). However, a paired samples t-test shows that this difference in mean blood cholesterol levels

( = 5.15, *sd = *18.66) is not significant, *t*(25) = 1.41, *p* = .172. The 95% confidence interval indicates that on average, cholesterol levels are between 2.39mg/dL higher and 12.69mg/dL lower after sterols are added to the diet.

There is insufficient evidence to conclude that there is a difference in the blood cholesterol levels after the introduction of sterols into the diet.

* Correlation and Regression*It was hypothesised that people with more experience would tend to earn higher salaries.

–

In a random sample of 30 Australians with full time employment, there was a moderate strength, positive, linear relationship between length of experience and weekly salary, and Pearson’s

*r*shows that this relationship is significant,

*r*= .65,

*n*= 30,

*p*ρ = .32 and

*ρ =*.54. In the sample, for each additional year of experience, on average, respondents earned an extra $28.06 per week.

As expected, people with more experience tend to earn higher salaries.

-It was hypothesised that longer bushwalks would take more time.

In a random sample of 40 bushwalks, there was a weak, negative, linear relationship between distance walked and time taken (in hours), and Pearson’s *r* shows that this relationship is significant, *r* = –.37, *n* = 40, *p = *.021. The 95% confidence interval for Pearson’s correlation indicates that the strength of the relationship is between *ρ = *–.06 and *ρ = *–.61. In the sample, for each additional kilometre walked, on average, the time taken to complete the walk was 0.05 hours less.

Contrary to expectations, longer bushwalks tend to take less time.

-It was hypothesised that students with higher IQs would tend to have better exam scores.

In a random sample of 100 students, there was an extremely weak, positive, linear relationship between IQ and exam scores. However, Pearson’s *r* indicates that this relationship is not significant, *r* = .03,* n* = 100, *p = *.341. The 95% confidence interval indicates that the strength of the relationship is between *ρ* = –.17 and *ρ* = .23.

There is insufficient evidence to suggest that there is a relationship between IQ and exam scores.

* Crosstabulations*It was hypothesised that people who use generic brands of toilet paper are more likely to scrunch than people who use Kleenex or Quilton.

–

In a sample of 71 students, those who used generic brand toilet paper were the most likely to scrunch followed by users of Kleenex. While 60% of generic brand users scrunched, 31% of Kleenex users and only 16% of Quilton users scrunched. The relationship between brand of toilet paper and scrunch/fold choice was significant,

^{2(2) = 8.75, p = .013. As expected, users of generic brand toilet paper are more likely to scrunch than users of Kleenex or Quilton.}

-It was suggested that people with a tertiary education are less likely to own a Mac home computer than people with a secondary education.

In a sample of 200 people who own a home computer, those with a tertiary education were actually more likely to own a Mac than those with a secondary education. While 26% of participants with a tertiary education owned a Mac, only 13% of participants with a secondary education owned a Mac. The relationship between education level and type of computer owned is significant, 2(1) = 5.31, *p = *.021.

Contrary to expectations, people with a tertiary education are more likely to own a Mac than people with a secondary education.

-It was hypothesised that fulltime students are more likely to participate in sport twice a week than part time students.

In a sample of 217 students, there was no significant relationship between enrolment status and level of participation in sport, 2(2) = 1.34, *p = *.512.

There is insufficient evidence to suggest that fulltime students are more likely to participate in sport twice a week than part time students.