Question

1. State the Null and Alternative
2. Find The Standard error and Test statistics (show work for credit ) include the decoding.
3. Draw the standard normal Distribution and decide how likely is the test statistics.
4. Decide to reject or accept the Null hypothesis ~ Use the Test statistics and or the p-value. Show or describe where did you get the p-value if use it.
5. Conclusion

A group of researchers wanted to investigate the effect that active listening have in feeling understood. The researchers know from prior studies (using the FUME scale: feeling of understanding scale) that the results of interaction with partners who received advice from the listener had a FUME average score 11.79 with the standard deviation of 7.47. The researchers conducted an experiment where the 37 participants were given an interaction partner and that partner engaged actively listened without given any advice. The result of that experiment showed that mean FUME score was 17.27. Is the enough evidence to suggest that active listening without given advice produce a different mean FUME score of feeling understood?

Answer 1

Here the claim is that mean is different from 11.79

So hypothesis is vs

Now as population standard deviation is known we will use z statistics

The z-critical values for a two-tailed test, for a significance level of α=0.05

zc​=−1.96 and zc​=1.96

Graphically

As test statistics falls in the rejection region we reject the null hypothesis

P value is

As P value is less than alpha=0.05 (as it is not given we assume it to be 0.05)

Hence we have sufficient evidence to support the claim that mean is different from 11.79