Let X equal the thickness of spearmint gum manufactured

QUESTION:

Let \(X\) equal the thickness of spearmint gum manufactured for vending machines. Assume that the distribution of \(X\) is \(N\left(\mu, \sigma^{2}\right)\). The target thickness is \(7.5\) hundredths of an inch. We shall test the null hypothesis \(H_{0}: \mu=7.5\) against a two-sided alternative hypothesis, using 10 observations.

(a) Define the test statistic and critical region for an \(\alpha=\) \(0.05\) significance level. Sketch a figure illustrating this critical region.

(b) Calculate the value of the test statistic and state your decision clearly, using the following \(n=10\) thicknesses in hundredths of an inch for pieces of gum that were selected randomly from the production line:

(c) Is \(\mu=7.50\) contained in a \(95 \%\) confidence interval for \(\mu\) ?

Equation Transcription:

Text Transcription:

X  

N(mu,sigma^2)

7.5  

H_0:mu =7.5  

Alpha = 0.05  

n=10  

mu=7.50  

95%

mu