Please help with problem number 28. It's geometry.
1 answer:
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Answer:
: p= .78
: p > .78
Step-by-step explanation:
Determining the null and alternate hypotheses of a scenario require several components. The first is if one should use p or mu. This depends on if they are assessing a proportion or a mean, since the publisher states a percentage, you know that they are asking for a proportion, and therefore should use p. Next, they will need to assess what value to use for the hypothesis statements, here only .78 is provided and therefore should be used in both. Finally, it is time to add in the comparison symbols, the null hypothesis always uses an equals sign so it therefore becomes:
: p= .78
The alternate hypothesis then needs to consider if the researchers claim that the new proportion is greater, fewer, or different. In this case it is greater as they think that the ownership is above 78%, so a greater than sign would be used and the final statement would be:
: p > .78
Answer:
B. Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
35 gas ovens
A consumer group has determined that the distribution of life spans for gas ovens has a mean of 15.0 years and a standard deviation of 4.2 years. This means that:
40 electric ovens.
The distribution of life spans for electric ovens has a mean of 13.4 years and a standard deviation of 3.7 years.
Which of the following best describes the sampling distribution of barXG - bar XE, the difference in mean life span of gas and electric ovens?
By the Central Limit Theorem, the shape is approximately normal.
Mean:
Standard deviation:
So the correct answer is given by option b.