Question

calibrating a scale: making sure that the scales used by businesses in the united states are accurate is the responsibility of the national institute for standards and technology (nist) in washington, d.c. suppose that nist technicians are testing a scale by using a weight known to weigh exactly 1000 grams. the standard deviation for scale reading is known to be σ = 2.2. they weigh this weight on the scale 52 times and read the result each time. the 52 scale readings have a sample mean of x̄ = 1000.5 grams. the calibration point is set too high if the mean scale reading is greater than 1000 grams. the technicians want to perform a hypothesis test to determine whether the calibration point is set too high. use the α = 0.01 level of significance and the p - value method with the ti - 84 plus calculator. part: 0 / 5 part 1 of 5 (a) state the appropriate null and alternate hypotheses. h₀: h₁: this hypothesis test is a select test.

Explanation:

Step1: Define Hypotheses

The null hypothesis \( H_0 \) is that the mean scale reading is equal to 1000 grams, so \( H_0: \mu = 1000 \). The alternative hypothesis \( H_1 \) is that the mean scale reading is greater than 1000 grams (since we want to test if calibration is too high), so \( H_1: \mu > 1000 \). This is a right - tailed test.

Step2: Identify Test Type

Since we are testing a claim about the population mean, and the population standard deviation \( \sigma = 2.2 \) is known, we can use a z - test (for a single population mean with known standard deviation). But for the hypothesis setup, the key is the form of the hypotheses.

Answer:

\( H_0: \boldsymbol{\mu = 1000} \)
\( H_1: \boldsymbol{\mu > 1000} \)
This hypothesis test is a right - tailed test.