Question: ARE THERE HUMAN PHEROMONES? This exercise examines studies introduced on page 11 about human pheromones, which are chemical signals given off that may subconsciously influence others. In the studies, men had a pad attached to their upper lip that contained either tears collected from women who watched sad films or a salt solution (as a placebo) that had been trickled down the same women's faces. The studies follow a double-blind matched pairs design. The order was randomized, and the difference in responses under the two conditions (Placebo response – Tears response) was recorded. This exercise involves a test for a single mean, where the data is the difference in responses. Show all details: hypotheses, sample statistic, p-value, and conclusion in context.
Do Tears Subconsciously Affect Sadness Ratings? After exposure to either tears or a placebo, men were shown pictures of female faces and asked "To what extent is this face sad?" The difference in ratings between the two treatments is in HumanTears25, and is available on StatKey. Use StatKey or other technology to see if the data provide evidence that tears contain a chemical signal affecting perceptions of sadness. In particular, test to see if we can conclude that the mean difference in ratings is not equal to zero.
State the null and alternative hypotheses.
H₀: μ = 0 vs Hₐ: μ ≠ 0
The hypothesis input area is centered in the lower-middle of the page; the graph/input panel is in the center, and the text block above is at top-left.Give notation of the sample statistic.
Sample statistic:
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Give value of the sample statistic accurate to two decimal places.
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Use a randomization distribution to find the p-value. Give your answer accurate to two decimal places.StatKey Randomization Test for a Mean
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Randomization Dotplot of x̄. Null hypothesis: μ = 98.6
Left Tail
Two-Tail
Right Tail
0.025
0.950
0.025
98.390
98.801
samples = 1000
mean = 98.599
std. error = 0.100
Original Sample
n = 50, mean = 98.26
median = 98.2, stdev = 0.765
98.26
Randomization Sample
Show Data Table
n = 50, mean = 98.58
median = 98.54, stdev = 0.61
98.58
null = 98.6
top-left: a large randomization dotplot of x̄ spanning roughly 98.28 to 98.95 on the x-axis and 0 to 90 on the y-axis, with black stacked dots forming a mound centered near 98.6, red x marks in both tails, and labels 0.025, 0.950, 0.025 above the left tail, center, and right tail regions; the null value is marked at 98.6 near the bottom axis.
top-right: an Original Sample dotplot with x-axis about 96.5 to 101.0 and y-axis 0 to 40, showing brown points clustered around 98 to 99.5 and a label line indicating 98.26.
bottom-right: a Randomization Sample dotplot with x-axis about 96.5 to 101.0 and y-axis 0 to 40, showing brown points clustered around 98 to 99.5 and a label line indicating 98.58.help me solve this statistics problem
1. **State the problem:** We want to test if tears subconsciously affect sadness ratings by comparing the mean difference in ratings (Placebo response – Tears response) to zero.
2. **Hypotheses:**
- Null hypothesis $H_0$: $\mu = 0$ (no difference in mean sadness ratings)
- Alternative hypothesis $H_a$: $\mu \neq 0$ (there is a difference in mean sadness ratings)
3. **Sample statistic notation:** The sample mean difference is denoted as $\bar{x}$.
4. **Sample statistic value:** From the data, the sample mean difference is $\bar{x} = 98.26$ (given).
5. **Randomization distribution:** The null hypothesis assumes $\mu = 0$, so the randomization distribution is centered at zero difference.
6. **Calculate p-value:** Using the randomization test, the p-value is the probability of observing a sample mean difference as extreme or more extreme than $98.26$ under $H_0$.
7. **Interpretation:** If the p-value is less than the significance level (commonly $0.05$), we reject $H_0$ and conclude that tears affect sadness ratings.
8. **Conclusion:** Based on the randomization test and p-value (which should be calculated using StatKey or similar), we determine if there is evidence that tears contain a chemical signal affecting sadness perception.
Note: The exact p-value is not provided in the prompt; use StatKey or software to find it accurately.