Exam 13: Tests of Hypotheses: Standard Deviations

If the hypothesis $\sigma=0.20$ is tested against the hypothesis that $\sigma \neq 0.20$ , with $\alpha=0.05$ , based on a random sample of size $n=18$ , then the appropriate tabled value(s) is(are)

If $\alpha=0.10$ , the hypothesis that $\sigma_{1}=\sigma_{2}$ , the sample variances $s_{1}^{2}=18$ and $s_{2}^{2}=54$ were obtained, based on sample sizes of $n_{1}=15$ and $n_{2}=10$ respectively, the null hypothesis should be

In order to convert a small-sample confidence interval for the variance to a confidence interval for the standard deviation we must __________.

A hypothesis test involving one population standard deviation sometimes involves the calculation of $x^{2}=\frac{(n-1) s^{2}}{\sigma^{2}}$ .

It is always true that the higher the value of $\chi^{2}$ the more likely the null hypothesis that $\sigma=28$ will be rejected.

The value of the standard deviation $\sigma_{0}$ is never obtained from a sample.

If $\frac{s_{1}^{2}}{s_{2}^{2}}$ has a value very close to 0 , then the null hypothesis of equal population standard deviations cannot be rejected.

An owner of a chain of supermarkets claims that there is greater price competition among supermarkets than among small "convenience" food stores. A sample of ground beef prices in 13 supermarkets and 10 convenience stores gives standard deviations of $\$ 0.15$ and $\$ 0.10$ , respectively. Evaluate the claim at the $10 \%$ significance level.

When finding a confidence interval for $\sigma^{2}$ , based on small sample, the number of degrees of freedom for the chi-square distribution is __________.

In tests concerning the equality of two population variances, the test statistic is __________.

In testing the null hypothesis that a population standard deviation equals a specified constant, the value $\sigma_{0}$ is the hypothesized standard deviation.

If a significance level of 0.01 is used in testing the null hypothesis that $\sigma=0.30$ against the alternative that $\sigma>0.30$ , based on a random sample of size $n=15$ , then the relevant tabled value is

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of $\mathbf{0 . 6 0}$ . -Find a $95 \%$ confidence interval for the population variance.

In testing the null hypothesis that a population standard deviation equals a specified constant based on a small sample, the test statistic that is used is __________.

A sample estimate of $\sigma$ is symbolized by __________.

In an effort to evaluate the hypothesis that $\sigma_{1}=\sigma_{2}$ , the sample variances $s_{1}^{2}=18$ and $s_{2}^{2}=54$ were obtained, based on sample sizes of $n_{1}=15$ and $n_{2}=10$ , respectively. The numerator and denominator degrees of freedom are, respectively,

Calculate the $F$ ratio for the set of data and compare it to the appropriate tabled value. Make a decision concerning the null hypothesis of equal population standard deviations. - $s_{1}=15 \quad n_{1}=16$ $s_{2}=7 \quad n_{2}=10$ $\alpha=0.02$

The mean of chi-square distribution is equal to __________.

The more that the sample standard deviation $s$ differs from the hypothesized value $\sigma_{0}$ , the more likely that the null hypothesis

The possible values that a chi-square distribution can assume are __________.