Hypothesis testing

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   A researcher wants to test whether the mean sugar content of a cereal differs from $\mu_0 = 18$ grams per serving, setting up $H_0: \mu = 18$ against $H_1: \mu \ne 18$. The population standard deviation is unknown. A random sample of $n = 19$ servings has sample mean $\bar x = 17$ grams and sample standard deviation $s = 5$ grams. Compute the test statistic $t = \dfrac{\bar x - \mu_0}{s/\sqrt n}$, rounded to 2 decimal places.

2. Warm-up

   A researcher wants to test whether the mean sugar content of a cereal differs from $\mu_0 = 30$ grams per serving, setting up $H_0: \mu = 30$ against $H_1: \mu \ne 30$. The population standard deviation is unknown. A random sample of $n = 38$ servings has sample mean $\bar x = 29.50$ grams and sample standard deviation $s = 2$ grams. Compute the test statistic $t = \dfrac{\bar x - \mu_0}{s/\sqrt n}$, rounded to 2 decimal places.

3. Warm-up

   A researcher wants to test whether the mean sugar content of a cereal differs from $\mu_0 = 29$ grams per serving, setting up $H_0: \mu = 29$ against $H_1: \mu \ne 29$. The population standard deviation is unknown. A random sample of $n = 29$ servings has sample mean $\bar x = 32$ grams and sample standard deviation $s = 6.50$ grams. Compute the test statistic $t = \dfrac{\bar x - \mu_0}{s/\sqrt n}$, rounded to 2 decimal places.

Problems shown under their original terms: Generated (template, solver-computed).