Statistical Inferences Based on Two Samples Essay

8. Draw conclusions – Assuming that your experiment produced results identical to those seen in Table 4, would you reject or accept the hypothesis that you produced in question 3? Explain how you determined this.

This corresponds to a two-tailed z-test for proportions. The z-statistics is computed by the following formula:

So, we should reject the null hypothesis H0. At a 0.05 level of significance level, we conclude that there is a significant difference between the average height for females and the average height for the males.

 Inferential statistics helps us to analyze predictions, inferences, or samples about a specific population from the observations that they make. “With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone” (Trochim, 2006). The goal for this type of data is to review the sample data to be able to infer what the test group may think. It does this by making judgment of the chance that a difference that is observed between the groups is indeed one that can be counted on that could have otherwise happened by coincidence. In order to help solve the issue of generalization, tests of significance are used. For example, a chi-square test or T-test provides a person with the probability that the analysis’ sample results may or may not represent the respective population. In other words, the tests of significance provides us the likelihood of how the analysis results might have happened by chance in a scenario that a relationship may not exist between the variables in regards to the population that is being studied.

Topics Distribution of the sample mean. Central Limit Theorem. Confidence intervals for a population mean. Confidence intervals for a population proportion. Sample size for a given confidence level and margin of error (proportions). Poll articles. Hypotheses tests for a mean, and differences in means (independent and paired samples). Sample size and power of a test. Type I and Type II errors. You will be given a table of normal probabilities. You may wish to be familiar with the follow formulae and their application.

If the total sample size is over 15, two sample t tests are safe if there are no

There is a null hypothesis and an alternative hypothesis. The null hypothesis usually states there is no difference and an alternative hypothesis states there is. A result is positive if it rejects the null hypothesis. A result is negative if it does not reject the null

5. The standard deviations of the groups are different between these two data sets. This implies that both girls and the boys groups have a large variability in their data. The reason is that the standard deviation for boys is 5.9 and the standard deviation for girls is 5.0. This means the data has a wide range of data within the mean.

1. A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general population. A random sample of 90 students at a private high school is tested and and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (σ= 200).

In a one-way ANOVA, the null hypothesis tested by rather the population means are equal, or that each of the group means is equal. If the null hypothesis is rejected, then it can be concluded that at least one of the population means is different from at least one other population mean. The alternative hypothesis, however, looks to see that at least two of the group means are significantly different. The assumption of independence is obtained if the observations are random and independent if they are to be representative of the populations and in no way related or dependent on another. The distributions of the populations from which the samples are selected are normal; This is commonly referred as the assumption of normality. The variances of the distributions in the populations are equal. This is often referred as the assumption of homogeneity of variance.

“Hypothesis testing is a decision-making process for evaluating claims about a population” (Bluman, 2013, p. 398). This process is used to determine if you will accept or reject the hypothesis. The claim is that the bottles contain less than 16 ounces. The null hypothesis is the soda bottles contain 16 ounces. The alternative hypothesis is the bottles contain less than 16 ounces. The significance level will be 0.05. The test method to be used is a t-score. The test statistic is calculated to be -11.24666539 and the P-value is 1.0.  The P-value is the probability of observing a sample statistic as extreme as the test statistic, assuming the null hypothesis is true. The T Crit value is 1.69912702. The calculations show there is enough evidence to support the claim that the soda bottles do

Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of

Conclusion : Reject the null hypothesis. The sample provide enough evidence to support the claim that mean is significantly different from 12 .

c.  Then find the 95% confidence interval for the difference between proportions.   From this confidence interval, can we conclude that there is a significant difference in the proportions?

Assumption 3 is homogeneity of variance, that the variances of the outcome variable in both groups, the male group and the female group, will be equal. The Levene Test for Equality of Variances has a sig. value of .566. This number is higher than .05 and, therefore, implies that the variability of the two groups is about equal.