Nikki wishes to test the hypothesis that bird feeders can affect the mean mass of birds in the area surrounding the feeder. She weighs several of the hummingbirds near several feeders. She obtains 4.2, 3.9, 3.6, 3.5, 3.9, 3.8, 3.8, 4.1, 3.9, 3.8, 3.2, and 3.4 as masses in grams for the birds. The student's hypotheses are Ho: H = 3.65 g and H3: µ> 3.65 g. Use technology to calculate the P-value, then determine whether the data provide sufficient evidence to conclude that the mean mass of the birds in the area surrounding the feeder is greater than the mean mass of the general population. Test at the 5% significance level and assume that the population standard deviation is 0.35 g. Also, assess the strength of the evidence against Ho. O A. P=0.255; since P> 0.05, reject the null hypothesis. The data do provide sufficient evidence to conclude that the mean mass of the birds in the area is greater than the mean mass of the general population. The evidence against the null hypothesis is moderate. O B. P= 0.509; since P> 0.05, reject the null hypothesis. The data do provide sufficient evidence to conclude that the mean mass of the birds in the area is less than the mean mass of the general population. The evidence against the null hypothesis is strong. C. P=0.1418; since P> 0.05, do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean mass of the birds in the area is greater than the mean mass of the general population. The evidence against the null hypothesis is weak or none.
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.
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