1). Dr. Johnson hypothesizes that people who practice yoga for one hour a day will have higher scores on a life satisfaction test than those in the general population. On a standard life satisfaction test, the overall population mean, or , is 88.3 and the standard deviation, ors, is 6.4. The researcher gives this same test to a random sample of 24 individuals who regularly practice yoga for at least one hour a day. Their sample mean () is 90.5, with a sample s of 5.5.

• H₀:
• H_A:

What is your z_critical value? Is this a one-tailed or two-tailed test?

What is the obtained z value?

Numerator =

Standard error of the mean (denominator) =

z =

Apply your decision rule: Compare your obtained z with your critical z. Does it fall in the region of rejection or not? Do you reject or fail to reject the null hypothesis?

Explain your results? Do people who practice yoga have higher life satisfaction scores than people in the general population?

Part II: Single-sample t-tests

Like the ztest, the single sample t-test is used to test a sample against a population to determine if the means from each are significantlydifferent from one another. However, we use the single-sample t-test when the population variance is not known. The formulas below are used to calculate the estimatedstandard error of the mean and the overall t.

1). A researcher hypothesizes that individuals who listen to classical music will score differently from the general population on a test of spatial ability. On a standardized test of spatial ability, the population mean, or , is 58. A random sample of 14 individuals who listen to classical music is given the same test with a sample mean of 59 and a sample s of 3.80.

H₀:

H_A:

What is your t_critical value given your degrees of freedom (N-1)? See page 433.

What is the obtained t value?

Numerator =

Estimated standard error of the mean (denominator) =

t =

Apply your decision rule: Compare your obtained t with your critical t. Does it fall in the region of rejection or not? Do you reject or fail to reject the null hypothesis?

Explain your results? Do people who listen to classical music have different spatial ability scores compared to people in the general population?

Part III: Does Music Convey Social Information to Infants?

NOTE. I have provided the output for you! Focus on interpreting these result.

This final test uses the open data from Experiment 1 of Mehr, Song, and Spelke (2016). Note. in SPSS, the p-value (Called Sig.) tells you the probability that you obtained your results by chance. The number should be < .05 in order to reject the null hypothesis. This means that the probability your results are due to chance is less than 5%.

STUDY DESCRIPTION

Research by Mehr, Song, and Spelke (2016) sought to explore the psychological function that music has for parents and infants, by examining the hypothesis that particular melodies convey important social information to infants.

The authors argue that melodies are shared within social groups. Whereas children growing up in one culture may be exposed to certain songs as infants (e.g., "Rock-a-bye Baby"), children growing up in other cultures (or even other groups within a culture) may be exposed to different songs. Thus, when a new person (someone who the infant has never seen before) sings a familiar song, it may signal to the infant that this new person is a member of his or her social group.

To test this hypothesis, the researchers recruited 32 infants and their parents to complete an experiment.

During their first visit to the lab, the parents were taught a new lullaby (one that neither they nor their infants had heard before). The experimenters asked the parents to sing the new lullaby to their child every day for the next 1-2 weeks.

Following this 1-2 week exposure period, the parents and their infant returned to the lab to complete the experimental portion of the study. Infants were first shown a screen with side-by-side videos of two unfamiliar people, each of whom were silently smiling and looking at the infant. The researchers recorded the looking behavior (or gaze) of the infants during this 'baseline' phase. The looking behavior of babies is typically measured in order to determine if a baby likes or is interested in a stimulus. Babies will look longer at a preferred stimulus.

Next, one-by-one, the two unfamiliar people on the screen sang either the lullaby that the parents learned or a different lullaby (that the babies had never heard before). Finally, the infants saw the same silent video used at baseline, and the researchers again recorded the looking behavior of the infants during this 'test' phase. See figure 1 below for an example of the stimuli.

ANALYSES

Baseline refers to the proportion of time (.20 or 20%, .50 or 50%) the babies spent looking at the singer BEFORE she sang the familiar or unfamiliar melody. At baseline the babies should show NO PREFERENCE for one face over the other. In other words, the proportion of time spent looking at either face should be .50 or 50% because there are two faces.

The TEST variable refers to the proportion of time the babies spent looking at the face that sang the familiar melody - the one the parents had sung to the baby for the 2 weeks prior. The researchers hypothesized that the babies would show a preference for the person singing the familiar lullaby over the unfamiliar tune. The proportion of time spent looking at the face should be more than 50%.

Step 1: State your hypotheses...

Based on the study description, state your hypothesis about the proportion of time the babies will spend looking at the face that sings the familiar melody (at test)?

H₀:

H_A:

Step 2: Collect your data.

(See above for a description of how these data were collected.)