Question

Assume that a simple random sample has been selected from a normally distributed population and given claim. Identify the null and alternative hypothesis, test statistic, P-value, critical value(s), and state the final conclusion that addresses the original claim.

In a manuel 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 242.1 sec and a standard deviation of 56.78 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?

identify the test statistic.

t = ____ (round to two decimal places as needed)

Answer 1

The test statistic t is approximately 3.57 (rounded to two decimal places).

The test statistic for testing a hypothesis about a population mean when the population standard deviation is unknown and the sample size is less than 30 is given by:

t =
`(x - \mu_0)/((s)/(√(n) ) )`

Where:

x is the sample mean (242.1 seconds)

`\mu_0` is the hypothesized population mean (210 seconds)

s is the sample standard deviation (56.78 seconds)

n is the sample size (40)

Let's plug in the values:

t= ​
`(242.1- 210)/((56.78)/(√(40) ) )`

Calculating this gives:

t≈
`(32.1)/(8.998) = 3.57`

So, the test statistic t is approximately 3.57 (rounded to two decimal places).