Cats are visual animals and enjoy watching on-line videos. A newon-line video enhanced for feline viewing is being developed. Themean time that a cat will view the video in one setting is understudy. The nine cats in the study viewed the video for 82 secondson average with a standard deviation 18 seconds. Use thisinformation to answer the questions below.
- What is the parameter in this situation?
- What is the point estimate for the parameter in this case?
- What is the standard error for the point estimator in thiscase?
- What is the set of hypotheses that would be used to test thatthe mean viewing time is 90 seconds against the alternative thatthe mean viewing time differs from 90 seconds?
- What is the value of the test statistic to test the nullhypothesis that the mean viewing time is 90 seconds?
- What is the name of the distribution of the test statistic ifthe mean viewing time really is 90 seconds? This is the set ofvalues possible for the test statistic when the null hypothesis istrue.
- What value must the test statistic be more extreme than inorder to reject the null hypothesis at the 1% significancelevel?
- What is the value of the p-value in this case? State a range ofvalues, not a specific value. Hint: The p-value is the tail areasassociated with the test statistic, that is the area below thenegative and the area above the positive.
- What is the decision about the null hypothesis in this casewith a significance level of 1%? Hint: If the p -value is less thanthe significance level then reject the null hypothesis. The p-valueis the chance that you are wrong if you reject the null hypothesisbased on these data.
- What is the conclusion about the alternative hypothesis, basedon the decision above about the null hypothesis? Write a sentencethat begins, Conclude, the data… .
- What is the 99% confidence interval to estimate the parameterbased on these data?
- Does the above confidence interval contain the hypothesizedparameter value in this case? Write a sentence about what theconfidence interval indicates about the parameter value.