Assume that a simple random sample has been selected from a normally distributed

Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null a 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, t is stated that a song must be no longer than 210 seconds. A simple random sample of current hit songs results in a mean length of 220.2 sec and a standard deviation of 53.23 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? ( Click the icon to view the Minitab display. What are the hypotheses? Ho : = 210 sec H1:-210sec Ho : = 210 sec H1: s 210 sec OB Ho:

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 210
Alternative hypothesis: > 210

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 8.42
DF = n - 1

D.F = 39
t = (x - ) / SE

t = 1.21

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 1.21.

Thus the P-value in this analysis is 0.117

Interpret results. Since the P-value (0.117) is greater than the significance level (0.05), we cannot reject the null hypothesis.

A) Fail to reject H0, there is insufficient evidence to support the claim that the sample is from population of songs with mena length greater than 210.

The research do not suggest that the advice of writing a song that must be longer than 210 seconds is not sound advice.

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