Question

2. Consider an assembly line that packs candies into retail packages. The weight of packages has a normal distribution $N(\mu, 6^2)$. When the assembly line is working properly, the average weight of packages is 500g. 16 retail packages are examined to check if the assembly line is working properly. Their weights are 495, 505, 506, 497, 512, 492, 498, 503, 502, 510, 506, 508, 494, 492, 501, 499 Note the average weight of this batch is 502g. Further assume the variance remains the same. Use hypothesis testing to test if the assembly line is working properly at $\alpha = 0.05$. (a) (4 points) State the null/alternative hypotheses with appropriate parameter in the population. (b) (4 points) State the test statistic you will use and its distribution. Compute the test statistic based on the data. (c) (4 points) Formulate your decision rule based with rejection region. (d) (4 points) At $\alpha = 0.05$, what is your conclusion? You might find these values useful $z_{0.05} =$ 1.64, $z_{0.025} = 1.96$, $z_{0.01} = 2.33$.

          2. Consider an assembly line that packs candies into retail packages. The weight of packages has a normal
distribution $N(\mu, 6^2)$. When the assembly line is working properly, the average weight of packages is
500g. 16 retail packages are examined to check if the assembly line is working properly. Their weights
are
495, 505, 506, 497, 512, 492, 498, 503, 502, 510, 506, 508, 494, 492, 501, 499
Note the average weight of this batch is 502g. Further assume the variance remains the same.
Use hypothesis testing to test if the assembly line is working properly at $\alpha = 0.05$.
(a) (4 points) State the null/alternative hypotheses with appropriate parameter in the population.
(b) (4 points) State the test statistic you will use and its distribution. Compute the test statistic based
on the data.
(c) (4 points) Formulate your decision rule based with rejection region.
(d) (4 points) At $\alpha = 0.05$, what is your conclusion? You might find these values useful $z_{0.05} =$
1.64, $z_{0.025} = 1.96$, $z_{0.01} = 2.33$.

2. Consider an assembly line that packs candies into retail packages. The weight of packages has a normal
distribution N(μ, 6^2). When the assembly line is working properly, the average weight of packages is
500g. 16 retail packages are examined to check if the assembly line is working properly. Their weights
are
495, 505, 506, 497, 512, 492, 498, 503, 502, 510, 506, 508, 494, 492, 501, 499
Note the average weight of this batch is 502g. Further assume the variance remains the same.
Use hypothesis testing to test if the assembly line is working properly at α = 0.05.
(a) (4 points) State the null/alternative hypotheses with appropriate parameter in the population.
(b) (4 points) State the test statistic you will use and its distribution. Compute the test statistic based
on the data.
(c) (4 points) Formulate your decision rule based with rejection region.
(d) (4 points) At α = 0.05, what is your conclusion? You might find these values useful z0.05 =
1.64, z0.025 = 1.96, z0.01 = 2.33.

Added by Erin R.

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