Question

The average low temperature for Doha in November is claimed to be greater than 20oF. The low temperatures of 8 randomly selected days in November are measured. The sample average is calculated to be 23oF with a standard deviation of 4 oF.

1-Test the claim at 10% significance level.

2-Calculate the 90% lower confidence bound

Answer 1

1.

Suppose, random variable X denotes low temperature in a day for Doha in November.

We have sample values. But we do not know population standard deviation (or variance). So, we have to perform one sample t-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Sample size

Sample mean

Sample standard deviation

Degrees of freedom

[Using R-code '1-pt(2.12132,7)']

Level of significance

We reject our null hypothesis if

Here, we observe that

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that there is significant evidence that the average low temperature for Doha in November is greater than .

2.

We have sample values. But we do not know population standard deviation (or variance). So, we have to use test statistic corresponding to one sample t-test.

Corresponding test statistic is given by

Here,

Sample size

Sample mean

Sample standard deviation

Degrees of freedom

Level of significance

We have,

  [Using R-code 'qt(1-0.90,7)']

Hence, 90% lower confidence bound is 20.999.