The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 55 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Find the test statistic to see whether the candy bars are smaller than they are supposed to be
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To determine whether the candy bars are smaller than they are supposed to be, we can use a hypothesis test.
First, let's establish the null and alternative hypotheses:
Null hypothesis (H0): The candy bars are not smaller than they are supposed to be.
Alternative hypothesis (Ha): The candy bars are smaller than they are supposed to be.
To conduct this hypothesis test, we will use the z-test, as we have the population standard deviation (0.77 gm) and a large enough sample size (49).
The test statistic for a z-test is calculated using the formula:
z = (x - μ) / (σ / √n)
where:
x is the sample mean (55.82 gm)
μ is the population mean (55 gm)
σ is the population standard deviation (0.77 gm)
n is the sample size (49)
Substituting the values into the formula, we get:
z = (55.82 - 55) / (0.77 / √49)
z = 0.82 / (0.77 / 7)
z = 0.82 / 0.11
z ≈ 7.45
Therefore, the test statistic for this hypothesis test is approximately 7.45 (rounded to two decimal places).
To determine the conclusion of the hypothesis test (whether the candy bars are smaller than they are supposed to be), we would compare the calculated test statistic with the critical value(s) based on the desired significance level and the appropriate statistical distribution (in this case, the standard normal distribution for a z-test).