Question

1. Scores on the belief in UFO’s test are normally distributed with m = 40 with a standard deviation of 3. Higher scores indicate greater belief in UFO’s. A sample of 24 people is forced to watch every episode of the X-Files TV show and then completes the test. The sample has a mean score of 46. Does watching the X-Files increase people’s belief in UFO’s? Use a = .01.

1a.       The hypothesis test should be...                                              (highlight one) (1 point)

                        a) one-tailed (directional)      b) two-tailed (non-directional)                       

           

1b. According to your answers above, conduct the hypothesis test.

Step 1:

State your hypotheses in symbols. (Be sure to label H0 and H1.)

State your hypotheses in words. (Be sure to label H0 and H1.)

Step 2: Set up the criteria for making a decision.   

Step 3: Compute the appropriate test-statistic.

According to your answers above, what is your conclusion? Does watching the X-Files increase belief in UFO’s?

            a) Yes

            b) No

1c. Based on your answer above, what type of error might you have made in your decision in Step 4?                                                                                                                            

Answer 1

Solution:-

1a.) (A) The hypothesis test should be one-tailed (directional).             

1b)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 40
Alternative hypothesis: u > 40

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), and the z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 0.6124

Step 2)

z_Critical = 2.326

Rejection region z > 2.326
Step 3)

z = (x - u) / SE

z = 9.80

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesised population mean, and n is the sample size.

Interpret results. Since the z-value (9.80) lies in the rejection region, hence we have to reject the null hypothesis.

a) Yes, watching files increases belief in UFO's.

1c) Type I error.