1.

Suppose that a random variable X is normally distributed with mean 74 and standard deviation 28. If a random sample of size 36 is taken, what is the z value when the sample mean is 147? Please give your answer correctly rounded to two decimal places.

Answer:

2.

The management team of a large store is interested in the relationship between annual sales ($000) and the opening times (hours) of different franchise stores. The following regression output summarises the findings for a sample of franchise stores.

Regression Statistics
Multiple R	0.7
R square	0.49
Adjusted R square	0.4655
Observations	79

	Coefficients
Intercept	237.7
Opening times	2.3

How many observations were used to create this regression?

Answer:

3.

In an effort to assist with annual electricity costs ($000), a large number of households in Australia have installed solar panels. To investigate this, a researcher took a random sample of households recording the annual electricity cost and the number of solar panels per household. Excel was used to MAKE A simple linear regression of annual electricity cost against solar panels, with a portion of the regression output provided here:

Regression statistics
Multiple R	0.75
R square	0.5625
Observations	163
	Coefficients	Standard Error
Intercept	1.93	8.25
Solar panels	1.36	2.09

State the correlation coefficient.

Please give your answer correctly rounded to two decimal places.

Answer:

4.

Parts a) and b) are NOT related. All are compulsory.

a) A newspaper journalist is researching people's opinion on the removal of hand sanitiser stations in public places. The journalist took a random sample of 40 adults and found 4 individuals agreed with the removal of hand sanitiser stations in public places. Assume the conditions are satisfied and do NOT need to be checked here.

ii) Calculate a 95% confidence interval. SHOW BASIC WORKINGS.

iii) Interpret your confidence interval for the journalist.

b) A student made the following statement:

"The larger the sample size, the wider the confidence interval, all else held constant."

State whether you agree or disagree with this student.

Briefly explain the reasoning behind your answer.