Question

Collect and organize 2 samples of 30 items of data from a source you find relevant. (assume your values are normally distributed).Some examples:

Weather (average daily temperature for a month, max hurricane wind speed, etc.)

Find the mean, median, mode and range for each group.

Find the variance and standard deviation for each group.

Find the 95% confidence interval for the mean of each group.

Test the hypothesis that the means are different (.05 significance)

Answer 1

We take temperature of New York in two different months as below, also we calculate mean, median, mode, variance and standard deviation below the table.

Assuming the data are normally distributed, the 95% confidence interval for the mean of each group is given by:

95% Confidence interval for January will be (32.352, 32.715)

95% Confidence interval for March will be (41.346, 43.320)

HYPOTHESIS TESTING:

We assume that the actual mean temperature of January and March are and respectively. The observed means are and respectively.

Null Hypothesis i.e. the two means are equal. The test statistic is given by:

Under null hypothesis Z = -19.138

Hence the p-value will be

At 0.05 significance level, we have

Hence, we can reject the null hypothesis which says that the two means are same.

Hence, we can conclude that the two means are different at 0.05 level of significance