A sample of 27 blue M&Ms has a mean weight of 0.8560 grams. Assume that is known to be 0.0565 g. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the mean weight of all M&Ms is equal to 0.8535 grams (the weight necessary so that bags of M&Ms have the weight printed on the package).
a)What is the test statistic?
b)What is the critical value.
c)What is the P-value?
d)What is the conclusion about the null hypothesis (reject, fail to reject)?
e)Give the final conclusion in simple non-technical terms.
To get P = .05, Ho needs to have μ ± 1.96 SD, Reject Ho, if value is outside that range.
P is determined by Z score = (X-μ)/SD. Look up value in "area under normal distribution" in back of your stats text.
Is "that" your SD?
I hope this helps. If not, repost with more questions. Thanks for asking.
To answer these questions, we need to perform a hypothesis test using the given information.
Null hypothesis (H0): The mean weight of all M&Ms is equal to 0.8535 grams.
Alternative hypothesis (Ha): The mean weight of all M&Ms is not equal to 0.8535 grams.
a) The test statistic:
The test statistic for this hypothesis test is calculated using the formula:
test statistic = (sample mean - population mean) / (known standard deviation / sqrt(sample size))
Plugging in the given values:
test statistic = (0.8560 - 0.8535) / (0.0565 / sqrt(27))
b) The critical value:
The critical value is the value that divides the rejection region from the non-rejection region. Since the significance level is 0.05, we need to determine the critical value from the standard normal distribution table or using statistical software.
c) The P-value:
The P-value is the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true. To calculate the P-value, we compare the test statistic to the critical value using the t-distribution table or statistical software.
d) Conclusion about the null hypothesis:
If the P-value is less than the significance level of 0.05, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
e) Final conclusion in simple non-technical terms:
Based on the calculated test statistic, critical value, and P-value, if the P-value is less than 0.05, we reject the claim that the mean weight of all M&Ms is 0.8535 grams; otherwise, there is not enough evidence to reject the claim.