A manufacturer of sports equipment has developed a new synthetic fighting line, which he claims has

Izabella Ponce

Izabella Ponce

Answered question

2022-06-16

A manufacturer of sports equipment has developed a new synthetic fighting line, which he claims has a mean breaking strength of 15 pounds with a standard deviation of 0.5 pounds.
Test the hypothesis that μ = 15 pounds against the alternative that μ + 15 pounds, if a random sample of 50 lines is tested and found to have a mean breaking strength of 14.8 pounds.
Use a 0.01 level of significance.

Answer & Explanation

lilao8x

lilao8x

Beginner2022-06-17Added 22 answers

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A manufactueree of sports equipment has developed a new syhtetic fighting line, which he claims has a mean breaking strength of 15 pounds with a standard deviation σ=0.5 pounds.
Test the hypothesis, H o : μ = 15against the alternative hypothesis H 1 : μ 15
A random sample of 50 lines is tested and found to have a mean breaking strength of 14.8 pounds.
Use a 0.01 level of significance.\
The required calculation can be defined by the formula,
Set appropriate hypothesis
Choose the level of significance at 1%
The test statistic formula,
Z = x ¯ μ σ n N ( 0 , 1 )
standard deviation H 0 : μ = 15
The null hypothesis states that there is no significant difference between the population mean breaking strength
H 1 : μ 15
The alternative hypothesis states that there is a significant difference between the population mean breaking strength
To calculate the test statistics,
Z = 14.8 15 0.5 50 = 2.8289
the critical value:
Z 0.01 2 = 2.58
Since the Z >∣ Z a 2 then we can conclude that the null hypothesis is rejected.
P-value:
The P-value is p=0.0023 which is less than the level of significance 0.01, it is concluded that the null hypothesis is rejected
Conclusion:
The null hypothesis is rejected at 1% level of significance and we may conclude that there is a significant difference between the population mean breaking strength of pounds.

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