Question

Asked Oct 4, 2019

Step 1

**Hypotheses:**

*Null hypothesis:*

*H*_{0}: *µ* = 1.73

That is, the new toothpaste performs similar to main whitening toothpaste in preventing cavities.

*Alternative hypothesis:*

*H*_{1}: *µ* ≠1.73

That is, the new toothpaste performs is not similar to main whitening toothpaste in preventing cavities.

Since the alternative hypothesis states *µ* ≠1.73, this test is a **two-tailed** test.

Step 2

**Critical value:**

Consider the level of significance as 0.05.The critical value for 0.05 significance level is 1.96.

Step 3

**Calculation:**

It is given that *X *has a normal distribution and *σ* = 1.12.

Since it is assumed that *X *has a normal distribution with known *σ*, the standard normal is the appropriate sampling distribution.

*Test statistic for z-test:*

Here, the sample mean, *x*-bar is 1.5.

Population mean, *µ* is 1.73.

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