Question

Asked Apr 1, 2019

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Suppose 36 participants complete an experiment where ads are presented subliminally during a task (e.g. Coke ads are flashed at very fast rates during movie ads). Participants are then given a recognition test of images of the ads, where two images are presented and participants must choose which of the two was presented earlier. Both men and women (18 of each gender) participate in the study and the researcher predicts that the recognition accuracy will differ across gender.

The difference between the sample means in this study was 6%. The SS for the men was 250 and the SS for the women was 150.

What decision should the researcher make about the hull hypothesis in this study and what can the researcher conclude about their prediction from this decision?

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Step 1

**Test whether there is enough evidence to conclude that the mean recognition accuracy differs among men and women****:**

It is given that the sample size of men and women is *n*_{1} = *n*_{2} = 18.

The difference between the sample means is (*x*_{1}-bar – *x*_{2}-bar) = 0.06.

The sum of squared deviations *SS* for men is (*SS*)* _{men} *= 250 and the sum of squared deviations

Let μ_{1 }be the population mean recognition accuracy of men and μ_{2} be the population mean recognition accuracy of women.

*The hypotheses are given below:*

*Null hypothesis:*

*H*_{0} : μ_{1} = μ_{2}

That is, there is no significant difference between the mean recognition accuracy of men and the mean recognition accuracy of women.

*Alternative hypothesis:*

*H*_{1} : μ_{1} ≠ μ_{2} (Two tail test).

That is, there is a significant difference between the mean recognition accuracy of men and the mean recognition accuracy of women.

Step 2

**Find the sample standard deviations of men and women:**

*Sum of squared deviations:*

The sum of squared deviations indicates by how much the data points in the dataset vary from the given number (generally mean).

The general formula for sum of squared deviations from mean is,

*SS* = ∑(*X _{i}* –mean)

The general formula for standard deviation is,

*s* = SQRT(*SS*/*n *–1)

The standard deviation of men and women are obtained as **3.8348 and 2.9704 **from the calculation given below:

Step 3

**Obtain the sample t–score for the study:**

The sample size of men and women is *n*1 = *n*2 = 18,

The difference between the sample means is (*x*1-bar – *x*2-bar) = 0.06,

The standard deviation of men is *s*1 = 3.8348,

The standard deviation of women is *s*...

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