Question

At wind speeds above 1000 cm/sec significant sand-moving events begin to occur. In particular, wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large sand dunes. At one test site, the prevailing direction of the wind did not change. However, the speed did change. Sixty wind speed readings gave an average speed of 1075 cm/sec. From long term experience, it can be assumed that =265 cm/sec. Do these data indicate that sand is moving to new locations at this test site? Use 1. State the null and alternate hypotheses. What is the level of significance? 2. What is the value of the test statistic? 3. Find the -value. 4. Will you reject or not reject the null hypothesis? 5. State your conclusion in the context of the application.

Answer 1

Let : Average wind speed.

We have to test the claim that

Sand is moving to new loaction at the given test site.

1. Null hypothesis -

against

Alternative hypothesis- ( right-tailed test)

consider

Since level of significance not given

We consider Alpha: Level of significance = 0.05

2. Given :

Since population standard deviation is known, we use one sample z-test for testing population mean.

The value of test statistic z is

Value of test statistic z= 2.1923

3. Since the test is right-tailed and value of test statistic z is 2.1923

p-value is obtained by

p-value = P ( Z> 2.1923)

from normal probability table

P( Z> 2.1923) =0.0142

p-value = 0.0142

4. Since p-value < alpha, we reject the null hypothesis at 5% level of signifcance.

5. Conclusion : At 5% l.o.s. there is sufficient evidence to claim that Sand is moving to new loaction at the given test site.