Question

A zoologist thinks that adult male toads in N.Y. State have mean weight of 1.7 pounds. To test this notion, she takes a random sample of 38 adult male toads in N.Y. State and finds that the mean weight of 1.8 pounds. Assume from previous studies that standard deviation of the weights of adult male toads in N.Y. State is 0.4 pounds. Perform the test at the 10% level of significance.

Answer 1

Solution:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: adult male toads in N.Y. State have mean weight of 1.7 pounds.

Alternative hypothesis: Ha: adult male toads in N.Y. State have mean weight different than 1.7 pounds.

H0: µ = 1.7 versus Ha: µ ≠ 1.7

This is a two tailed test.

The test statistic formula is given as below:

Z = (x̄ - µ)/[σ/sqrt(n)]

From given data, we have

µ = 1.7

x̄ = 1.8

σ = 0.4

n = 38

α = 0.10

Critical value = ±1.6449

(by using z-table or excel)

Z = (1.8 - 1.7)/[0.4/sqrt(38)]

Z = 1.5411

P-value = 0.1233

(by using Z-table)

P-value > α = 0.10

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that adult male toads in N.Y. State have mean weight of 1.7 pounds.