Question

Bats are nocturnal mammals, feeding on insects at night and sleeping during the day. Many species of bats use bridges as daytime sleeping places. Their choice of daytime position on the undersurface of a bridge appears to be non-random. One theory is that the bats choose locations that will keep them safer from predators. The beams that support a bridge create two kinds of spaces: wide (approximately 55 cm) and narrow (approximately 17 cm); biologists believe the narrow spaces provide more safety. Investigators studying the sleeping position choices of the Big-eared Bat (Corynorhinus rafinesquii) observed that 57 out of 102 of them were in narrow beam spaces. The narrow beam spaces accounted for approximately 46% of the available area under the bridges. The investigators want to see if this sample provides sufficient evidence that the bats prefer narrow over wide sleeping space. What is the P-value for this test?

Answer 1

Solution:-

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

Null hypothesis: P = 0.50
Alternative hypothesis: P > 0.50

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.04951
z = (p - P) / S.D

z = 1.188

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 1.188.

P-value = P(z > 1.118)

Use z-score table or z-score calculator to compute p-value.

Thus, the P-value = 0.117.

Interpret results. Since the P-value (0.117) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do have sufficient evidence in the favor of the claim that the bats prefer narrow over wide sleeping space.