Do Babies Prefer Speech? Psychologists in Montreal and Toronto conducted a study to determine if babies show any preference for speech over general noise.1 Fifty infants between the ages of 4-13 months were exposed to both happy-sounding infant speech and a hummed lullaby by the same woman. Interest in each sound was measured by the amount of time the baby looked at the woman while she made noise. The mean difference in looking time was 27.79 more seconds when she was speaking, with a standard deviation of 63.18 seconds. Perform the appropriate test to determine if this is sufficient evidence to conclude that babies prefer actual speaking to humming. 1Corbeil, M., Trehub, S.E., Peretz, I., “Speech vs. singing; infants choose happier sounds,” Frontiers in Psychology, 25 June, 2013. State the null and alternative hypotheses. Use μ1 for μd in the response area. H0: vs. Ha: Calculate the relevant test statistic. Round your answer to three decimal places. t-statistic= Find the p-value. Round your answer to four decimal places. p-value = What is the conclusion? Reject H0. Do not reject H0. Do we have evidence to conclude that babies prefer speaking to humming? Yes No

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Do Babies Prefer Speech?

Psychologists in Montreal and Toronto conducted a study to determine if babies show any preference for speech over general noise.¹ Fifty infants between the ages of 4-13 months were exposed to both happy-sounding infant speech and a hummed lullaby by the same woman. Interest in each sound was measured by the amount of time the baby looked at the woman while she made noise. The mean difference in looking time was 27.79 more seconds when she was speaking, with a standard deviation of 63.18 seconds. Perform the appropriate test to determine if this is sufficient evidence to conclude that babies prefer actual speaking to humming.

¹Corbeil, M., Trehub, S.E., Peretz, I., “Speech vs. singing; infants choose happier sounds,” Frontiers in Psychology, 25 June, 2013.

State the null and alternative hypotheses.

Use μ1 for μd in the response area.

H₀: vs. H_a:

Calculate the relevant test statistic.

Round your answer to three decimal places.

t-statistic=

Find the p-value.

Round your answer to four decimal places.

p-value =

What is the conclusion?

Reject H0.

Do not reject H0.

Do we have evidence to conclude that babies prefer speaking to humming?

Yes

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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