The null hypothesis,H0:u=48,was tested against the alternative hypothesis,H1:u>48.A sample of 75 resulted in a calculated p-value of 0.102.if standard deviation=3.5,the value of the sample mean is?need help

Using the z-test formula, solve for sample mean:

z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

Find z in a z-table using p-value. Population mean is 48. Standard deviation is 3.5 and sample size is 75.

I'll let you take it from here.

To determine the value of the sample mean, we need more information about the test statistic used. The calculated p-value alone does not provide enough information to directly determine the sample mean.

However, if you know the test statistic used (such as t-test or z-test), we can proceed with the calculation. Let's assume it was a z-test.

In a z-test, we compare the sample mean to a known population mean (in this case, 48) using the formula:

z = (X - μ) / (σ / √n)

Where:
X is the sample mean
μ is the population mean
σ is the standard deviation
n is the sample size

Given that the standard deviation (σ) is 3.5, and the sample size (n) is 75, and the null hypothesis (H0) states that μ = 48, we can rearrange the formula to solve for the sample mean (X):

X = z * (σ / √n) + μ

To find the value of the sample mean, we first need to find the critical value (Zα) corresponding to the p-value of 0.102. The critical value helps in determining whether to reject or fail to reject the null hypothesis.

Assuming a significance level (α) of 0.05 (commonly used), the critical value for a one-tailed test can be obtained using a z-table or statistical software.

If the calculated z-value exceeds the critical value (Zα), we would reject the null hypothesis and consider the alternative hypothesis (H1) to be true.

Please provide the critical value for a one-tailed test using a significance level (α) of your choice, or any additional information about the test statistic used to proceed with the calculation of the sample mean.