Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative? hypotheses, test? statistic, P-value, and state the final conclusion that addresses the original claim. In a manual on how to have a number one? song, it is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results in a mean length of 233.1 sec and a standard deviation of 54.22 sec. Use a 0.05 significance level and the accompanying Minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 sec. What do these results suggest about the advice given in the? manual? LOADING... Click the icon to view the Minitab display. What are the? hypotheses? A. Upper H 0?: muequals210 sec Upper H 1?: mugreater than210 sec B. Upper H 0?: mugreater than210 sec Upper H 1?: muless than or equals210 sec C. Upper H 0?: muequals210 sec Upper H 1?: muless than or equals210 sec D. Upper H 0?: muless than210 sec Upper H 1?: mugreater than210 sec

Answer 1

Solution:

Solution:

The provided sample mean is X¯ = 233.1 and the sample standard deviation is s = 54.22, and the sample size is n = 40

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: ? ? 210

Ha: ? > 210

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

Now use MINITAB to test above hypothesis,

Follow the following steps:

Click Stat ------> Basic Statistics --------> 1-Sample t...

You will be presented with the following 1-Sample t (Test and Confidence Interval) dialogue box:

Click on Summarized data and fill the information.

You get output:

t-stat = 2.695

p-value = 0.0052

Decision: Using the P-value approach: The p-value is p = 0.0052 and since p = 0.0052 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion: Therefore, there is enough evidence to claim that the population mean ? is greater than 210, at the 0.05 significance level.

Done