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Answer :
In hypothesis testing, the null hypothesis states that there is no significant difference between the observed sample mean and the claimed population mean. The P-value is approximately 0.0930, and at a significance level of 0.05, the conclusion is to fail to reject the null hypothesis.
The null hypothesis would be that the mean weight of women is 145 lbs.
To test this hypothesis, we calculate the P-value, which measures the probability of obtaining a sample mean as extreme as the one observed (or more extreme) assuming the null hypothesis is true. The P-value is compared to the chosen significance level to make a conclusion.
Given a sample of 40 weights of women with a mean weight of 153.2 lbs, we can use the sample mean and the population standard deviation (30.86 lbs) to calculate the test statistic, typically a t-statistic or z-score.
By conducting the appropriate calculations, the P-value is found to be approximately 0.0930. When comparing this value to the significance level of 0.05, we observe that the P-value is greater than the significance level. Therefore, we fail to reject the null hypothesis.
Based on these results, the correct answer is A: 0.0930. The P-value is not significant enough to reject the null hypothesis, indicating that there is not enough evidence to support a significant difference between the observed sample mean and the claimed population mean.
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