Question

it is claimed that a certain type of bipolar transistor has a mean value of current gain that is at least 120. a sample of these transistors is tested. if the sample mean value of current gain is 200 with a sample standard deviation of 35, would the claim be rejected at the 5 percent level of significance if the sample size is 25?

Answer 1

To determine if the claim is rejected, we need to perform a hypothesis test. The null hypothesis is that the mean value of current gain is 120, and the alternative hypothesis is that the mean value of current gain is greater than 120. After calculating the test statistic and comparing it to the critical value, we reject the null hypothesis and conclude that there is convincing evidence that the mean value of current gain is greater than 120 at the 5 percent level of significance.

Step-by-step explanation:

To determine if the claim is rejected, we need to perform a hypothesis test.

Step 1: State the null and alternative hypotheses. The null hypothesis is that the mean value of current gain is 120, and the alternative hypothesis is that the mean value of current gain is greater than 120.

Step 2: Select the level of significance. In this case, the level of significance is 0.05.

Step 3: Calculate the test statistic. The test statistic is the sample mean minus the hypothesized mean, divided by the standard deviation divided by the square root of the sample size. In this case, the test statistic is (200-120)/(35/sqrt(25)).

Step 4: Compare the test statistic to the critical value. Since the sample size is larger than 30, we can use a z-test. The critical value for a one-tailed test with a level of significance of 0.05 is 1.645. If the test statistic is greater than the critical value, we reject the null hypothesis.

In this case, the test statistic is greater than 1.645, so we reject the null hypothesis. Therefore, there is convincing evidence that the mean value of current gain is greater than 120 at the 5 percent level of significance.