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 000 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.
H2: bc = 0 vs H1: bc 2 0
Graph/location: the hypothesis input area is in the center of the page, with the math symbols and dropdown boxes in a centered panel.Give notation of the sample statistic.
Sample statistic:
eTextbook and Media
Give value of the sample statistic accurate to two decimal places.
eTextbook and Media
Use a randomization distribution to find the p-value. Give your answer accurate to two decimal places.StatKey
Randomization Test for a Mean
Body Temperature
Show Data Table
Edit Data
Upload File
Change Column(s)
Generate 1 Sample
Generate 10 Samples
Generate 100 Samples
Generate 1000 Samples
Reset Plot
Randomization Dotplot of x0. Null hypothesis: bc = 98.6
Left Tail
Two-Tail
Right Tail
samples = 1000
mean = 98.599
std. error = 0.100
0.025
0.950
0.025
98.390
null = 98.6
98.801
Original Sample
n = 50, mean = 98.26
median = 98.2, stdev = 0.765
Randomization Sample
Show Data Table
n = 50, mean = 98.58
median = 98.54, stdev = 0.61
98.58
Main plot: a randomization dotplot centered around 98.6 with black dots forming a bell-shaped cluster from about 98.30 to 98.90, red x marks in both tails, and tail cutoffs labeled 98.390 on the left and 98.801 on the right, position_hint = center
Top-right plot: Original Sample dotplot with points spread roughly from 96.5 to 101.0 and a marker at 98.26, position_hint = top-right
Bottom-right plot: Randomization Sample dotplot with points spread roughly from 96.5 to 101.0 and a marker at 98.58, position_hint = bottom-rightUser: help me
1. **State the problem:** We want to test if human tears subconsciously affect sadness ratings by men. The data is the difference in sadness ratings between placebo and tears conditions.
2. **Hypotheses:**
$$H_0: \mu = 0$$ (no difference in mean sadness ratings)
$$H_a: \mu \neq 0$$ (mean sadness ratings differ)
3. **Sample statistic:** Let $\bar{x}$ be the mean difference in ratings (Placebo - Tears). The sample mean $\bar{x}$ is given (from data) accurate to two decimals.
4. **Randomization distribution:** Use a randomization test to simulate the distribution of $\bar{x}$ under $H_0$.
5. **Calculate p-value:** The p-value is the probability of observing a sample mean as extreme or more extreme than the observed $\bar{x}$ under $H_0$. Use the randomization distribution to find this.
6. **Conclusion:** If p-value $< 0.05$, reject $H_0$ and conclude tears affect sadness ratings. Otherwise, do not reject $H_0$.
Since exact sample mean and p-value are not provided here, use StatKey or software to input the data and obtain:
- Sample mean $\bar{x}$ (e.g., $-0.25$)
- p-value (e.g., $0.03$)
If p-value $= 0.03 < 0.05$, conclude there is evidence that tears subconsciously affect sadness ratings.
**Summary:**
- Null hypothesis: $\mu = 0$
- Alternative hypothesis: $\mu \neq 0$
- Sample mean difference: $\bar{x} = $ (value from data)
- p-value: (value from randomization test)
- Conclusion: (reject or fail to reject $H_0$) in context of tears affecting sadness perception.