When working with individuals with phobias, we often have them rate their fear o

Question

When working with individuals with phobias, we often have them rate their fear on a scale of 1 (low) to 100 (high). We take 15 random samples across the US of non-phobic individuals and measure their level of fear to snakes. Results show that, when taking the average of these 15 samples, these individuals expressed a mean fear level of “30” with a standard deviation of 22. However, when we look at 15 individuals with an actual snake phobia, they reported a mean fear level of “50”. Is this meaningfully different from what non-phobic samples reported?

1)Formulate a null hypothesis and explain it. What would be the alternative hypothesis?

2)Test your hypothesis using a significance level of .05 and a two-tailed test. Show your work.

3)Based on the results you obtained, what do you conclude statistically? Do these groups seem different?

Explanation / Answer

The provided sample mean is X¯=30 and

sample standard deviation is s=22, and

sample size is n = 15.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: = 50 Vs. Ha: 5050

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used and n is small ( n<30)

(2) Rejection Region

Based on the information provided, the significance level is =0.05, and the critical value for a two-tailed test is tc=2.145.

The rejection region for this two-tailed test is R={t:t>2.145}

(3) Test Statistics

The t-statistic is computed as follows:

t = [ (X¯0) /( s/n) ] = [ (3050) / (22/15) ] = 3.521

(4) Decision about the null hypothesis

Since it is observed that t=3.521>tc=2.145, it is then concluded that the null hypothesis is rejected.

The p-value is p=0.0034, and since p=0.0034 < 0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean is different than 50, at the 0.05 significance level. So given group are seem different.

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