Answer :
1) The correct decision is to reject the null hypothesis (option c). 2) The 95% confidence interval for the sample of 25 students is 10 +/- 0.39 (option d).
When comparing the sample Z score to the cutoff Z score on the comparison distribution, we can determine the appropriate decision. In this case, the sample Z score is 1.95, which exceeds the cutoff Z score of +/- 1.64.
This indicates that the sample Z score falls within the critical region, where we reject the null hypothesis. Therefore, the correct decision is to reject the null hypothesis (option c).
For the 95% confidence interval, we can calculate it by taking the sample mean (10) and adding/subtracting the margin of error.
The margin of error is determined by multiplying the standard error (standard deviation divided by the square root of the sample size) by the critical value (corresponding to the desired confidence level).
With a sample size of 25, a standard deviation of 1, and a desired confidence level of 95%, the critical value is approximately 1.96. Calculating the margin of error (1 * 1.96 / √25) gives us 0.39. Thus, the 95% confidence interval is 10 +/- 0.39 (option d).
A 99% confidence interval of a mean tells us that 99% of similar experiments will include the true mean.
This means that if we were to repeat the study multiple times, 99% of the resulting confidence intervals would contain the true population mean. Therefore, option a is the correct explanation.
Learn more about confidence interval here: https://brainly.com/question/32546207
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The complete question is:
If the cutoff Z score on the comparison distribution is +/- 1.64 and the sample Z score is 1.95, the correct decision is to: a) Fail to accept the research hypothesis b) Fail to reject the null hypothesis c) Reject the null hypothesis d) Accept the research hypothesis What is the 95% confidence interval for a sample of 25 students with an average quiz score of 10 and a standard deviation of 1? a) 10 +/- 1 b) 25 +/- 10 c) 39 +/- 10 d) 10 +/-.39 A 99% confidence interval of a mean tells us that: a) 99% of similar experiments will include the true mean b) We can be 99% sure that our study does not include the true mean c) We have used a z value of 1.96 in our confidence interval calculation d) 99% of the population of interest has been included in our study
