[Inequalities] Please help and thanks.
2 answers:
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Answer:
Yes. The male and female consumers differ in the amounts they spend.
Step-by-step explanation:
We can express the null and alternative hypothesis as:
It is assumed a significance level of 0.05.
The standard deviation of the difference of means is calculated as:
The test statistic is
The degrees of freedom are:
The P-value for t=10.11 is P=0, so it is smaller than the significance level. The null hypothesis is rejected.
We can conclude that male and female consumers differ in the amounts they spend.
Answer:
0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean 490 mg and variance of 400.
This means that
What is the probability that a randomly selected pill contains at least 500 mg of minerals?
This is 1 subtracted by the p-value of Z when X = 500. So
has a p-value of 0.6915.
1 - 0.6915 = 0.3085
0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals