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 and alternative hypothesis, test statistic, P-value, and state the final conclusion that addresses the original claim:

In 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 234.4 seconds and a standard deviation of 57.32 seconds. Use a 0.05 significance level and the accompanying statdisk to test the claim that the sample is from a population of songs with a mean greater than 210 seconds.

Statdisk info: P-value: 0.0052 90% confidence interval: 219.1298 < u < 249.6702

a. express the original claim in symbolic form b. identify the null hypothesis c. identify the alternative hypothesis d. what is the value of alpha(significance level)? e. what is the sampling distribution of the sample statistic? (t,z, or chi square) f. is the test two tailed, left tailed, right tailed? g. what is the value of the test statistic? h. what is the p-value? i. what are the critical values? j. interpret using the p-value method k. interpret using the critical value method.

Explanation / Answer

b.The null hypothesis is: H0:mu=210 (The population mean is 210 seconds)

c.The alternative hypothesis is: H1:mu>210 (The population mean is greater than 210 seconds)

d.The significance level alpha=0.05

e. The sampling distribution of the sample statistic is t, as the population standard deviation is unknown.

f.The test is right tailed.

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