use SPSS to calculate the 90%, 95% and 99% confidence intervals for the mean of the variable weight. Interpret the three confidence intervals in terms of whether there is a significant difference between the mean of the sample and a hypothesized mean of 150.
Sample data missing.
For the value needed, find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of the outliers on each of both ends (.05, .025, .005) and the Z score.
90% = mean ± 1.645 SEm
95% = mean ± 1.96 SEm
99% = mean ± 2.575 SEm
SEm = SD/√n
To calculate the confidence intervals for the mean of the variable weight using SPSS, you can follow these steps:
1. Open your dataset in SPSS.
2. Go to the "Analyze" menu.
3. Select "Descriptive Statistics" and then choose "Explore".
4. In the "Explore" dialog box, select the variable "weight" from the list of variables and move it to the dependent list.
5. Under the "Options" button, check the "Confidence intervals" box.
6. Set the desired confidence level by selecting the appropriate options (90%, 95%, or 99%) from the "CIs for Mean" drop-down menu.
7. Click "OK".
SPSS will then calculate the confidence intervals for the mean of the variable weight at the specified confidence level. The output will include the lower and upper bounds of each confidence interval.
Now, let's interpret the three confidence intervals in terms of whether there is a significant difference between the mean of the sample and a hypothesized mean of 150.
- The 90% confidence interval provides a range within which we can be 90% confident that the population mean falls. If the hypothesized mean of 150 falls within this confidence interval, we cannot reject the null hypothesis that the population mean is equal to 150 at a 10% significance level. In other words, there is no significant difference between the mean of the sample and the hypothesized mean of 150 at a 10% significance level.
- The 95% confidence interval provides a range within which we can be 95% confident that the population mean falls. Similarly, if the hypothesized mean of 150 falls within this confidence interval, we cannot reject the null hypothesis that the population mean is equal to 150 at a 5% significance level. There is no significant difference between the mean of the sample and the hypothesized mean of 150 at a 5% significance level.
- The 99% confidence interval provides a wider range within which we can be 99% confident that the population mean falls. If the hypothesized mean of 150 falls within this confidence interval, we cannot reject the null hypothesis that the population mean is equal to 150 at a 1% significance level. There is no significant difference between the mean of the sample and the hypothesized mean of 150 at a 1% significance level.
In summary, if the hypothesized mean of 150 falls within any of the calculated confidence intervals, we do not have enough evidence to conclude that there is a significant difference between the mean of the sample and the hypothesized mean at the corresponding confidence level.