Final answer:
To conduct a hypothesis test on car parts reliability, one must assume a binomial distribution and set up null and alternative hypotheses. The test statistic is calculated and compared against the critical value or p-value to either reject or fail to reject the null hypothesis, considering a level of significance.
Step-by-step explanation:
To conduct a hypothesis test on car parts and reliability, you need to assume a binomial distribution since there are only two outcomes: pass or fail. Given 1 out of the 10 parts failed, you are testing if the failure rate is less than 7%. The null hypothesis (H0) would be that the failure rate is 7% or higher, and the alternative hypothesis (Ha) would be that the failure rate is less than 7%. Steps to perform the hypothesis test would include:
- Setting up the null and alternative hypotheses.
- Calculating the test statistic using the sample data.
- Determining the correct distribution, which would be the binomial or normal distribution (approximation if np and n(1-p) are both > 5).
- Comparing the test statistic to the critical value or p-value.
- Making a decision to reject or not reject the null hypothesis based on the level of significance.
In this case, we use binomial distribution since the sample size is small (n = 10). Alternatively, if np and n(1-p) were both over 5, we could use the normal approximation to the binomial distribution. Here, as 10*0.07 = 0.7 and 10*(1-0.07) = 9.3, both are not greater than 5 hence normal approximation would not apply. The test statistic can be calculated, and compared with the binomial probabilities to determine if the evidence is strong enough to reject the null hypothesis and conclude that the failure rate is less than 7%.