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The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is $s=0.37$. We want to Test the hypothesis $H_{0}:σ=0.25$ against $H_{1}=σ=0.25$, where $σ$ is the population standard deviation of the percentage of titanium in the alloy: - 1). Is this a $Z$, $T$ or $x_{2}$ test? State any necessary assumptions about the underlying distribution of the data. (2pts) - 2.) What is the observed value of the test statistic? (2pts) - 3.) Conclude the test by p-value method. (2pts) - 4.) Conclude the test by critical value method. (2pts) - 5). Explain how you can conclude the test by constructing a two-sided confidence interval on $σ$. (2pts)

1. Yes, this is a hypothesis test. The necessary assumption about the underlying distribution of the data is that the distribution of the percentage of titanium in the alloy is approximately normal. 2. The observed value of the test statistic can be calculated using the formula: test statistic (t) = (sample mean - hypothesized mean) / (sample standard deviation / ?sample size) In this case, the hypothesized mean is 0.25, the sample standard deviation is 0.37, and the sample size is 51. However, the sample mean is not provided in the information given, so the observed value of the test statistic cannot be determined without the sample mean.

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