Answer to Question #100036 in Statistics and Probability for Tannah

Question

A random sample of 128 firms was selected to investigate the average amount spent on liability insurance. The sample mean was found to be £25,500 per annum with a sample standard deviation equal to £3,250.
(i) Calculate the 95% confidence interval for the population mean.
(4 marks)
(ii) Calculate the 99% confidence interval for the population mean.
(4 marks)
(b) Discuss any four non probability sampling methods.

Answer 1

Here we have $\bar{X}=25500,n=128$ and $\sigma=3250$

i) Confidence interval is:

$\bar{X}\pm z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n}}$

Here, we have to find $95\%$ confidence interval, so $\alpha=0.05$

Now, the value of $z_\frac{\alpha}{2}$ Can be calculated using normal distribution table, which comes out to be $1.96$

So, the confidence interval will be

$25500\pm 1.96*\frac{3250}{\sqrt{128}}$

$25500\pm 6370/\sqrt{128}$

$25500\pm 563.033$

$=[24936.967,26063.033]$

ii) Confidence interval is:

$\bar{X}\pm z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n}}$

Here, we have to find $99\%$ confidence interval, so $\alpha=0.01$

Now, the value of $z_\frac{\alpha}{2}$

Can be calculated using normal distribution table, which comes out to be 2.58

So, the confidence interval will be

$25500\pm 2.58*\frac{3250}{\sqrt{128}}$

$25500\pm 8385/\sqrt{128}$

$25500\pm 741.1363$

$[24758.8637,26241.1363]$

b)

Non-probability sampling represents a group of sampling techniques that help researchers to select units from a population that they are interested in studying. Some of them are:

Quota sampling: With proportional quota sampling, the aim is to end up with a sample where the strata (groups) being studied (e.g., males vs. females students) are proportional to the population being studied.

Convenience sampling: A convenience sample is simply one where the units that are selected for inclusion in the sample are the easiest to access.

Purposive sampling: Purposive sampling, also known as judgmental, selective or subjective sampling, reflects a group of sampling techniques that rely on the judgement of the researcher when it comes to selecting the units.

Self selection sampling: Self-selection sampling is appropriate when we want to allow units or cases, whether individuals or organisations, to choose to take part in research on their own accord.