Question

Part 1 The world's smallest mammal is the bumblebee bat. The mean weight of 60 randomly selected bumblebee bats is 1.659 grams, with a standard deviation of 0.264 grams. Find a 99.9% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal): (WebAssign will check your answer for the correct number of significant figures. , WebAssign will check your answer for the correct number of significant figures. ) Find a 99% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal): (WebAssign will check your answer for the correct number of significant figures. , WebAssign will check your answer for the correct number of significant figures. ) Find a 95% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal): (Web Assign will check your answer for the correct number of significant figures. , WebAssign will check your answer for the correct number of significant figures. ) Find an 80% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal): (WebAssign will check your answer for the correct number of significant figures. , WebAssign will check your answer for the correct number of significant figures. ) Part 2 Dr. Clifford Jones claims that the mean weight of bumblebee bats is 1.8 grams. We are interested in whether it's less than he claims. Using the t-distribution technique, is there evidence that bumblebee bats weight less on average than he claims, at each of the following levels? The degrees of freedom are df = The test-statistic t = (positive version of t, three places after decimal) = WebAssign will check your answer for the correct number of significant figures. Is there evidence at the 10% level that bumblebee bats weigh less on average than he claims?

Answer 1

Part 1

Let the random variable X = mean weight of bumblebee bats

The random variable X follows a normal distribution with

mean = 1.659 grams

standard deviation = 0.264 grams

99.9% confidence interval

The confidence interval for the mean is obtained using the formula,

The t critical value is obtained from t distribution table for significance level = 0.001 and degree of freedom = n -1 = 60-1=59.

99% confidence interval

The t critical value is obtained from t distribution table for significance level = 0.01 and degree of freedom = n -1 = 60-1=59.

95% confidence interval

The t critical value is obtained from t distribution table for significance level = 0.05 and degree of freedom = n -1 = 60-1=59.

80% confidence interval

The t critical value is obtained from t distribution table for significance level = 0.20 and degree of freedom = n -1 = 60-1=59.

Part 2

Answer:

The degrees of freedom are df = 59

The test-statistic | t | =4.137

There is significant evidence at the 10% level that bumblebee bats weigh less on average than he claims.

Explanation:

The null and alternative hypotheses are defined as,

This is a left-tailed test

The significance level of the test = 0.10

The t critical value for the significance level =0.10 and degree of freedom = n - 1 = 59 is obtained from the t distribution table,

The t statistic is obtained using the formula,

Conclusion: Since the positive value of the t statistic is greater than the positive value of the t critical value, the null hypothesis is rejected hence there is sufficient to conclude that bumblebee bats weigh less on average than 1.8 grams.