Mathematics Homework Help

Overview

• In this assignment, you will compare the climate data from two different decades to see if there is statistical significant difference.
• You will calculate statistics on some climate data, and then use the statistics to calculate a test statistic and a p-value. You will use the p-value to conduct a hypothesis test and state the results.
• You will post all your results in the text entry or by uploading a document with the answers to this assignments. No graphs or images are required.
• I expect this assignment to take about 30 minutes
• Round your answers to three decimal places
  • For the p-value, you may have to go more than 3 decimal places, or write the answer as exponential notation, such as: 2.34E-6

Hypothesis

My claim is that the mean temperature in San Diego during the decade of the 1940’s was lower than the mean temperature for the most recent decade of the 2010’s.

This is a two-population hypothesis of the mean. Using the decade of the 1940’s as population 1 and the 2010’s as population 2, the following are the null and alternative hypotheses:

H0: 1= 2${\mu }_1={\mu }_2$

H1: 1< 2${\mu }_1<{\mu }_2$

Data

The temperature data for the two decades are in the following tables. The data represents the mean annual temperature for San Diego.

Population 1: 1940s

62.7
61.2
62.1
60.4
61.3
61.4
62.1
59.3
60.8
61.1

Population 1: 2010s

63.8
64.5
64.7
67.5
67.3
66.2
66.4
66.1
64.4
66.2

Test Statistic

In this step you will calculate statistics.

Use the t-distribution formula for two populations.

There are several ways to do these calculations on the calculator,

Formula

= ⎯⎯⎯⎯1− ⎯⎯⎯⎯2 21 1+ 22 2√$t=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$

TI-84 Calculator

2-SampTTest

StatCrunch

Stat -> T Stats -> Two Sample -> With Data

Report the following statistics in your submission. Round answers to 3 decimal places.

Population 1

Mean: ⎯⎯⎯1${\overline{x}}_1$

Standard Deviation: s1

Population 2

Mean: ⎯⎯⎯2${\overline{x}}_2$

Standard Deviation: s2

Test Statistic

P-Value

Calculate the p-value using the test statistic from the previous step and include this value in your report.

The answer may be very small, so you may have to include more than 3 decimal places or use scientific notation.

0.00000234

or

2.34E-6

TI-84 Calculator

tcdf

or 1-SampTTest

StatCrunch

Stat -> Calculator -> T

or Stat -> T Stats -> Two Sample -> With Data

Hypothesis Test

Use a significance level of =0.05$\alpha =0.05$ to perform a hypothesis test. Answer the two following questions:

Is the p-value less than or greater than the significance level?

Do you reject or fail to reject the null hypothesis.

Conclusion

State whether the data supports the claim that the mean temperature today is warmer than it was 80 years ago?

Summary

Include the following in your submission:

Population 1

Mean: ⎯⎯⎯1${\overline{x}}_1$

Standard Deviation: s1

Population 2

Mean: ⎯⎯⎯2${\overline{x}}_2$

Standard Deviation: s2

Test Statistic

P-Value

Hypothesis Test Questions

Conclusion

Criteria	Ratings	Pts
This criterion is linked to a Learning OutcomePopulation 1 StatsMean and Standard deviation for the first population. Accurate within 0.002		5 pts
This criterion is linked to a Learning OutcomePopulation 2 StatsMean and Standard deviation for the second population. Accurate within 0.002		5 pts
This criterion is linked to a Learning OutcomeTest StatisticTest Statistic is accurate within 0.002		5 pts
This criterion is linked to a Learning Outcomep-valuep-value is accurate within 0.002		5 pts
This criterion is linked to a Learning OutcomeHypothesis Test and ConclusionHypothesis test includes p-value and significance level Correct conclusion, reject or fail to reject Summary statement is appropriate and includes claim		5 pts
Total Points: 25