Question

I have compared the last 10 days of temperature highs in my current town and compared it with the last 10 days of temperature highs in Juneau, Alaska. Here were my results (in fahrenheit):

Derby Line:

27, 32, 34, 36, 28, 27, 32, 21, 32, 32

Juneau, Alaska:

37, 39, 37, 34, 28, 34, 36, 43, 39, 39

With the information I have provided, are we able to determine with 99% that Juneau, Alaska has a higher average temperature the last 10 days than where I live?

Answer 1

n1 = Sample size for Derby line = 10

= Sample mean for Derby line = 30.1

s1^2 = Variance for Derby line = 18.9889

n2 = Sample size for Juneau Alaska = 10

= Sample mean for Juneau Alaska = 36.6

s2^2 = Variance for Juneau Alaska = 16.2667

Claim: Juneau, Alaska has a higher average temperature for the last 10 days.

The null and alternative hypothesis is

: The population mean for Derby line

: The population mean for Juneau, Alaska

For doing this test first we have to check the two groups have population variances are equal or not.

Null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

F = 18.9889 / 16.2667 = 1.17

Degrees of freedom => n1 - 1 , n2 - 1 => 10 - 1 , 10 - 1 => 9 , 9

Critical value = 5.351   ( Using f table)

Critical value > test statistic so we fail to reject null hypothesis.

Conclusion: The population variances are equal.

So we have to use here pooled variance.

Test statistic is

Degrees of freedom = n1 + n2 - 2 = 10 + 10 - 2 = 18

Critical value = 2.552    ( Using t table)

| t | > critical value we reject null hypothesis.

Conclusion:

Juneau, Alaska has a higher average temperature for the last 10 days.