Consider the following hypotheses: H0: μ = 450 HA: μ ≠ 450 The population is normally distributed with a population standard deviation of 48. (You may find it useful to reference the appropriate table: z table or t table) a-1. Calculate the value of the test statistic with x−x− = 476 and n = 75. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) a-2. What is the conclusion at the 5% significance level? multiple choice 1 Do not reject H0 since the p-value is greater than the significance level. Do not reject H0 since the p-value is less than the significance level. Reject H0 since the p-value is greater than the significance level. Reject H0 since the p-value is less than the significance level. a-3. Interpret the results at αα = 0.05. multiple choice 2 We cannot conclude that the population mean differs from 450. We conclude that the population mean differs from 450. We cannot conclude that the sample mean differs from 450. We conclude that the sample mean differs from 450.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Consider the following hypotheses:
H0: μ = 450
HA: μ ≠ 450
The population is
a-1. Calculate the value of the test statistic with x−x− = 476 and n = 75. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
a-2. What is the conclusion at the 5% significance level?
multiple choice 1
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Do not reject H0 since the p-value is greater than the significance level.
-
Do not reject H0 since the p-value is less than the significance level.
-
Reject H0 since the p-value is greater than the significance level.
-
Reject H0 since the p-value is less than the significance level.
a-3. Interpret the results at αα = 0.05.
multiple choice 2
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We cannot conclude that the population
mean differs from 450. -
We conclude that the population mean differs from 450.
-
We cannot conclude that the sample mean differs from 450.
-
We conclude that the sample mean differs from 450.
b-1. Calculate the value of the test statistic with x−x− = 437 and n = 75. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
b-2. What is the conclusion at the 1% significance level?
multiple choice 3
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Do not reject H0 since the p-value is less than the significance level.
-
Do not reject H0 since the p-value is greater than the significance level.
-
Reject H0 since the p-value is less than the significance level.
-
Reject H0 since the p-value is greater than the significance level.
b-3. Interpret the results at αα = 0.01.
multiple choice 4
-
We cannot conclude that the population mean differs from 450.
-
We conclude that the population mean differs from 450.
-
We cannot conclude that the sample mean differs from 450.
-
We conclude that the sample mean differs from 450.
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