Can Dr. Easy Reject the Null Hypothesis in the EN-100 Test Analysis?

• lopram
In summary, Dr. Easy conducted a hypothesis test to determine if girls are smarter than boys on subjects tested by ACT. With a test statistic of 2.69 and a critical value of 1.701, she was able to reject the null hypothesis and conclude that the data supports the claim that girls are smarter than boys. The difference in means between boys and girls scores was not a determining factor in this conclusion.
lopram
Statistic Help!

I need some help solving this problem...

Dr. Easy saw the scores from the EN-100 test and used the occasion to test the old adage that girls are smarter than boys on subjects tested by ACT. Assume the degrees of freedom for this problem is 28. Dr. Easy did the arithmetic and found the value of the test statistic was 2.69 (alpha equals .05). What is the critical value (3 decimal places of significance)? If the mean of the boys score was lower than the mean of the girls score can she reject her null hypothesis? Yes or No.

Put:
$$H_0 :\mu_g\leq \mu_b$$
$$H_A :\mu_g> \mu_b$$ (Claim: girls are smarter than boys)

We have a right-tailed test, and I found on a table of critical t-scores that for df=28 and $$\alpha =.05$$ we have $$t_{.05 ;28} =1.701$$, which puts the test statistic of $$t=2.69$$ in the critical region so that we reject the null hypothesis $$H_0$$, and conclude that the data supports the claim that girls are smarter than boys.

If "the mean of the boys score was lower than the mean of the girls score" had much to do with this, I don't know why, other than telling us the sign of the test stastic (but we knew that).

To solve this problem, we need to use the t-test for independent samples. The null hypothesis (H0) states that there is no significant difference between the mean scores of boys and girls on the EN-100 test. The alternative hypothesis (H1) states that there is a significant difference between the mean scores of boys and girls on the EN-100 test.

To find the critical value, we need to look at the t-table for a two-tailed test with 28 degrees of freedom and a significance level of 0.05. The critical value is 2.048. Since the test statistic (2.69) is greater than the critical value, it falls in the rejection region. This means that we can reject the null hypothesis and accept the alternative hypothesis.

Since the mean of the boys' scores is lower than the mean of the girls' scores, this supports the alternative hypothesis, which states that there is a significant difference between the mean scores of boys and girls. Therefore, we can reject the null hypothesis and conclude that girls are, on average, smarter than boys on subjects tested by the ACT.

In conclusion, the critical value for this problem is 2.048 and we can reject the null hypothesis. The answer to the question "Can she reject her null hypothesis?" is Yes.

1. What is statistics and why is it important?

Statistics is the practice of collecting, organizing, analyzing, and interpreting data in order to make informed decisions. It is important because it helps us better understand and make sense of the world around us by providing quantitative evidence and insights.

2. How can statistics be applied in everyday life?

Statistics can be applied in many ways, such as in business, politics, healthcare, sports, and more. For example, statistics can help businesses make decisions about marketing strategies, politicians use polling data to understand public opinion, and doctors use statistics to evaluate the effectiveness of treatments.

3. What are some common statistical tools and techniques?

Some common statistical tools and techniques include descriptive statistics (mean, median, mode), inferential statistics (hypothesis testing, regression analysis), and data visualization (graphs, charts, tables).

4. How can I improve my understanding of statistics?

One way to improve your understanding of statistics is to practice solving problems and analyzing data. You can also take a statistics course, read books or articles on the subject, or seek help from a tutor or teacher.

5. How can statistics help me ace my EN-100 test?

By understanding and applying statistical concepts, you can analyze and interpret data effectively, which can help you answer test questions accurately. It is also important to review and practice specific concepts that will be covered on the test and seek help if needed.

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