Question

A story spoiler gives away the ending early. Does having a story spoiled in this way diminish suspense and hurt enjoyment? A study¹ investigated this question. For twelve different short stories, the study’s authors created a second version in which a spoiler paragraph at the beginning discussed the story and revealed the outcome. Each version of the twelve stories was read by at least 30 people and rated on a 1 to 10 scale to create an overall rating for the story, with higher ratings indicating greater enjoyment of the story. The ratings are given in Table 1 and stored in StorySpoilers. Stories 1 to 4 were ironic twist stories, stories 5 to 8 were mysteries, and stories 9 to 12 were literary stories. Test to see if there is a difference in mean overall enjoyment rating based on whether or not there is a spoiler.

Story	1	2	3	4	5	6	7	8	9	10	11	12
With spoiler	4.7	5.1	7.9	7.0	7.1	7.2	7.1	7.2	4.8	5.2	4.6	6.7
Original	3.8	4.9	7.4	7.1	6.2	6.1	6.7	7.0	4.3	5.0	4.1	6.1

Table 1 Enjoyment ratings for stories with and without spoilers

Find a 95% confidence interval for the difference in mean enjoyment rating between stories with a spoiler and stories without.

Click here for the dataset associated with this question.

Round your answers to three decimal places.

The 95% confidence interval is.....??????????

Answer 1

Using excel we carry out this analysis this problem is of two sample t test.

Using Excel Data Analysis toolpack we carryout this

Hypothesis:

Ho: There is a no difference in mean overall enjoyment rating based on spoiler and not spoiler.

V/s

H1: There is a difference in mean overall enjoyment rating based on spoiler and not spoiler.

Excel => Data => Data Analysis => t-Test: Two-Sample Assuming Equal Variances => input variables 1 and 2 => lables => ok

Story	With spoiler	Original
1	4.7	3.8
2	5.1	4.9
3	7.9	7.4
4	7	7.1
5	7.1	6.2
6	7.2	6.1
7	7.1	6.7
8	7.2	7
9	4.8	4.3
10	5.2	5
11	4.6	4.1
12	6.7	6.1

t-Test: Two-Sample Assuming Equal Variances
	With spoiler	Original
Mean	6.2167	5.725
Variance	1.4888	1.5784
Observations	12	12
Pooled Variance	1.5336
Hypothesized Mean Difference	0
df	22
t Stat	0.9725
P(T<=t) one-tail	0.1707
t Critical one-tail	1.7171
P(T<=t) two-tail	0.3414
t Critical two-tail	2.0739

Here p-value=0.3414 > alpha= 0.05 then we fail to reject Ho.

Conclude that, there is a no difference in mean overall enjoyment rating based on spoiler and not spoiler.

Now we have to find 95% confidance interval,

pooled standard deviation

	mean	sd	size	pooled sd
Spoiler	6.2167	1.2202	12	1.2384
Without spoiler	5.725	1.2563	12

Spoiler mean

Without spoiler

The 95% confidence interval is

[-0.557, 1.540]