Question

it is claimed that a certain type of bipolar transistor has a mean value of current gain that is at least 210. 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 (a) the sample size is 25; (b) the sample size is 64?

Answer 1

To determine if the claim that the mean value of current gain is at least 210 is supported or rejected, a hypothesis test is performed using the sample mean and standard deviation. The steps and calculations are outlined for both sample sizes.

Step-by-step explanation:

To determine whether the claim that the mean value of current gain is at least 210 is supported or rejected, we need to perform a hypothesis test. Let's break down the steps for each sample size:

(a) Sample size = 25:

1. Null hypothesis (H0): mean value of current gain = 210
2. Alternative hypothesis (Ha): mean value of current gain < 210 (since we want to test if the claim is rejected)
3. Compute the test statistic: z = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
4. Compare the test statistic with the critical value from the z-table or use p-value:

• If the test statistic is less than the critical value or the p-value is less than the significance level, we reject the null hypothesis
• If the test statistic is greater than the critical value or the p-value is greater than the significance level, we fail to reject the null hypothesis

Based on the result, determine whether the claim is supported or rejected.

(b) Sample size = 64:

1. Follow the same steps as in (a), but with the given sample size and values