Please write as neat as possible!!! A manufacturer of sports equipment claims th
ID: 3249374 • Letter: P
Question
Please write as neat as possible!!!
A manufacturer of sports equipment claims that its synthetic fishing line has a mean breaking strength of 8 kilograms. A random sample of 50 lines is tested and found to have a mean breaking strength of 7.8 kilograms. Does this data indicate that the population mean breaking strength is different than (either higher or lower than) 8 kilograms? Assume we are sampling from a normal population with standard deviation sigma = 0.5. Use a 0.01 level of significance. A) State the null hypothesis and the alternative hypothesis. B) Identify the rejection region. C) Compute the test statistic. D) Draw your conclusion. Is there sufficient evidence to conclude that the mean is different than 8? E) What is the p-value of the test statistic?Explanation / Answer
A)
Null Hypothesis : The population mean breaking is equal to 8.
Alternative Hypothesis: The population mean breaking is different than 8.
B) Rejection region from table
The rejection level at level of significance 0.01 is 2.58
C) Test Statistic:
SE = 0.5 / sqrt(50) = 0.07
Z = (7.8 - 8) / SE
= (7.8 - 8) / 0.07
= -2.85
D) Since the calculated value -2.85 falls beyond theinterval ( -2.57 , 2.57), hence we reject null hypothesis and conclude that their is a sufficient evidence to conclude that mean is differnt than 8.
E) P-value = 0.9978