Hi I need help with Statistics. Can anyone help me to understand it better? I am in fear that if I do not figure this out soon I will fail my class. I am needing help with the chapters 12,and 13. in the book called Statistical Reasoning in the Behavioral Sciences, 6th edition.
1. State whether each of the items in the list could be an alternative hypothesis and if so whether it would be a one tailed test or a two tailed test.
x- >345
µx≠12
x-=67
µx<89
x-<123
µx=45
µx>678
x-≠910
2. Two years ago, a complete survey of all male students in a large university indicated that the mean number of males that smoked per day was 8.3 with a standard deviation of 3.7. the director of the school wanted to see if the habits changed over the past two years. He got these results from the students: x- =7.7 n=108.
set up Ho and Ha
Perform the statical test (α =.05)
draw a conclusion.
3. the PTA at central H.S. is concerned that the students who graduate from the school do not score as well on the math test, on average, as do students from other school district. to address their concerns the principle randomly selected 15 students from the graduating class and administers the math teat used in that school district. the mean of the scores is 98. the scores of the 15 students from central high school are as follows: 105,98, 101, 110,96, 103, 104, 101, 98, 105, 112, 95, 105, 100, 108.
state formally the hypotheses necessary to conduct a nondirectional test
complete the test at the .05 level of significance and state your conclusion.
4.an industral/orginizational psychologist used a new training program designed to improve basic work shills. the traing program is typically judged as effective if average scores on a basic work skills test exceed 80. the psychologist obtained a random sample of participants who recently completed the training program, then administered to them a work skills test. their scores on the trest are givin in data 12A.
Data 12A
state the null and alt. hypothesis best suited to the nature of the psychologest inquiry
using IBM SPSS test the null hypothesis at the .01 level of significance and state your conclusion
5. with regard to Data 13A...
if α = .05 and µtrue=83.0 what is β
what is the power of the test?
if α=.01 and µtrue = 83.0 what is β
what is the power of the test?
Data 12A:
83 78 85 85 82 74 79 78 88 80 85 81 85 88 84 86 87 87 82 87 87 87 82 91 75 85 82 92 87 83 84 94 84 77 86 89 83 89 90 82 94 97 84 78 90 82 86 80 88 89 82 86 88 82 75 77 94 79 88 89
Data 13A:
Ho:µx= 80.0 Ha:µx≠80.0 σx=20.0 n=100
I'll give you a few hints.
The null hypothesis ALWAYS uses an equals sign. It could be greater than or equal to or less than or equal to or just equals some value.
An alternate hypothesis can be greater than, less than, or does not equal some value. If no direction is specified (does not equal), then the test is two-tailed. Otherwise, it is one-tailed.
For #2, try a one-sample z-test. Use a z-table to determine your critical value for a two-tailed test (the alternate hypothesis will not show a specific direction since the problem just wants to know if there is a change and that change could be in either direction). Compare the critical value to the test statistic. If the test statistic exceeds the critical value in either direction from the table, reject the null and conclude a change. If the test statistic does not exceed the critical value in either direction from the table, do not reject the null.
For #3, try a one-sample t-test since the sample size is rather small. Use a t-table to find the critical value for a two-tailed (nondirectional) test. Go through the same process as #2.
It looks like you are asked to use SPSS for #4. Try a z-test.
For #5, the alpha level directly affects the power of a test. Sample size also affects power. The test has greater power at .05 than .01.
Get an answer from tutors to this homework question now:have to: (a) Write the claim mathematically and identify H0 and Ha (b) Find the standardized test statistic Z and its corresponding area. (c) Find the P-value. (d) Decide whether to reject or fail to reject the null hypothesis. (e) Interpret the decision in the context of the original claim.
Sure, I can help you with your questions in Statistics. Let's go through each question one by one:
1. State whether each of the items in the list could be an alternative hypothesis and if so whether it would be a one-tailed test or a two-tailed test.
To determine if each item in the list could be an alternative hypothesis, we need to consider the form of the hypothesis and the nature of the test.
- x- > 345: This could be an alternative hypothesis for a one-tailed test, where we are interested in determining if the population mean (µx) is greater than 345.
- µx ≠ 12: This could be an alternative hypothesis for a two-tailed test, where we are interested in determining if the population mean (µx) is not equal to 12.
- x- = 67: This cannot be an alternative hypothesis since it is a specific value rather than a statement about the population mean.
- µx < 89: This could be an alternative hypothesis for a one-tailed test, where we are interested in determining if the population mean (µx) is less than 89.
- x- < 123: This cannot be an alternative hypothesis since it is a specific value rather than a statement about the population mean.
- µx = 45: This cannot be an alternative hypothesis since it is a specific value rather than a statement about the population mean.
- µx > 678: This could be an alternative hypothesis for a one-tailed test, where we are interested in determining if the population mean (µx) is greater than 678.
- x- ≠ 910: This cannot be an alternative hypothesis since it is a specific value rather than a statement about the population mean.
2. Two years ago, a complete survey of all male students in a large university indicated that the mean number of males that smoked per day was 8.3 with a standard deviation of 3.7. The director of the school wanted to see if the habits changed over the past two years. He got these results from the students: x- = 7.7, n = 108.
To set up the hypotheses (Ho and Ha), we need to determine the nature of the test and the direction of the alternative hypothesis.
- Ho (null hypothesis): The mean number of males that smoked per day has not changed over the past two years. µx = 8.3.
- Ha (alternative hypothesis): The mean number of males that smoked per day has changed over the past two years. µx ≠ 8.3.
To perform the statistical test at a significance level of α = 0.05, you would need to calculate the test statistic (e.g., t-statistic) and compare it to the critical value from the t-distribution (based on the degrees of freedom). Then, draw conclusions based on the test statistic and critical value.
3. The PTA at Central H.S. is concerned that the students who graduate from the school do not score as well on the math test, on average, as students from other school districts. The principal randomly selected 15 students from the graduating class and administered the math test used in that school district. The mean of the scores is 98. The scores of the 15 students from Central High School are as follows: 105, 98, 101, 110, 96, 103, 104, 101, 98, 105, 112, 95, 105, 100, 108.
To conduct a non-directional test, the hypotheses would be:
- Ho (null hypothesis): The average math test score for students at Central H.S. is the same as the average math test score for students in other school districts. µx = µother_districts.
- Ha (alternative hypothesis): The average math test score for students at Central H.S. is different from the average math test score for students in other school districts. µx ≠ µother_districts.
To complete the test at the α = 0.05 level of significance, you would need to calculate the test statistic (e.g., t-statistic) and compare it to the critical value from the t-distribution (based on the degrees of freedom). Finally, draw conclusions based on the test statistic and critical value.
4. An industrial/organizational psychologist used a new training program designed to improve basic work skills. The training program is typically judged as effective if the average scores on a basic work skills test exceed 80. The psychologist obtained a random sample of participants who recently completed the training program, then administered to them a work skills test. Their scores on the test are given in Data 12A.
To state the null and alternative hypothesis best suited to the nature of the psychologist's inquiry, we need to consider the desired outcome of the training program.
- Ho (null hypothesis): The average scores on the work skills test for participants who completed the training program are the same as or lower than 80. µx ≤ 80.
- Ha (alternative hypothesis): The average scores on the work skills test for participants who completed the training program are higher than 80. µx > 80.
To test the null hypothesis at the α = 0.01 level of significance using IBM SPSS (a statistical software), you would need to input the scores from Data 12A into SPSS and perform the necessary statistical test (e.g., one-sample t-test). Then, based on the test result (p-value), you can determine whether to reject or fail to reject the null hypothesis and state your conclusion accordingly.
5. For Data 13A, we need to calculate the values of β (type II error) and power of the test for different values of α and µtrue.
- If α = 0.05 and µtrue = 83.0, to calculate β, you would need additional information such as the standard deviation (σx), or the effect size, or the sample size (n), or the critical value for the corresponding test. Without this information, it is not possible to directly calculate β.
- To calculate the power of the test, you would need the significance level (α), the effect size (µtrue - µx), and additional information such as the standard deviation (σx), or the sample size (n), or the critical value for the corresponding test. Without this information, it is not possible to directly calculate the power of the test.
Similarly, for α = 0.01 and µtrue = 83.0, you would need additional information to calculate β and the power of the test.
Please provide the necessary information (e.g., standard deviation, sample size, critical value) for calculating β and the power of the test for Data 13A.