As the size of the sample n increases, the variable X¯ (it is a capital X with a hatch above) has an approximately normal distribution with greater dispersion between its values True or false?

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with s.d.= 2.3% . A random sample of 12 Australian bank stocks has a sample mean of x=6.16% . For the entire Australian stock market, the mean dividend yield is 7.2%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 7.2%? Find (or estimate) the P-value. Round your answer to three decimal places.

On average, a banana will last 6.1 days from the time it is purchased in the store to the time it is too rotten to eat.  Is the mean time to spoil greater if the banana is hung from the ceiling? The data show results of an experiment with 13 bananas that are hung from the ceiling. Assume that that distribution of the population is normal. 7.4, 7.5, 7.9, 5.7, 5.9, 8.1, 4.8, 8.7, 6.8, 5.9, 8.2, 5.1, 5.1 What can be concluded at the the αα = 0.10 level of significance level of significance?  For this study, we should use    Correct The alternative hypothesis would be:       H1:H1:     Correct      Correct Correct   The test statistic    Correct =  (please show your answer to 3 decimal places.) Based on this, we should     Correct the null hypothesis. Thus, the final conclusion is that ...

Suppose we have a normal distribution N(2, 4), using the Empirical rule, what proportion of data is between the data values -2 and 6?