cats are visual animals and enjoy watching online videos. a new online video enh
ID: 3341236 • Letter: C
Question
cats are visual animals and enjoy watching online videos. a new online video enhance for feline viewing is being developed. the mean time that I cat will view the video in one setting is under study. the nine cats in the study view the video for 82 seconds on average with a standard deviation of 18 seconds. use this information to answer the questions.
17. What is the decision about the null hypothesis in this case with a significance level of 1%? Hint If the p-value is less than the significance level then reject the null hypothesis. The p-value is the chance that you are wrong if you reject the null hypothesis based on these data 18. What is the conclusion about the alternative hypothesis, based on the decision above about the null hypothesis? Write a sentence that begins, Conclude, the data- 19, What is the 99% confidence interval to estimate the parameter based on these data? 20. Does the above confidence interval contain the hypothesized parameter value in this case? Write a sentence about what the confidence interval indicates about the parameter valueExplanation / Answer
n = 9
mean = 82 and sd = 18
we know that the z score is given as
Z = (X-Mean)/SD
9
You must provide X(the hypothesized parameter) too to perform the test , i shall asume the x to be 80 here
Z = (80-82)/(18/sqrt(9)) = -0.333
The p value for this z score from the z table is 0.369
as the p value is not less than 0.01 , hence we fail to reject the null hypothesis in favor of alternate hypothesis
now we know that the confidence interval is given as
mean +- z*sd/sqrt(n), where z is 2.59 for 99% CI from the z table
82 +- 2.59*18/sqrt(9)
82 - 2.59*18/sqrt(9) = 66.46
82 + 2.59*18/sqrt(9) = 97.54
This means that we are 99% confident that the true value of the mean lies between 66.46 and 97.54
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